Wave Motion 26 101 Exact complex source representations of transient radiation

贝雷砂岩研究

Geophysical Prospecting,2013,61,688–700doi:10.1111/j.1365-2478.2012.01110.x Experimental measurements of the streaming potentialand seismoelectric conversion in Berea sandstoneZhenya Zhu∗and M.Nafi Toks¨ozEarth Resources Laboratory,Dept.of Earth,Atmospheric,and Planetary Sciences,Massachusetts Institute of Technology,Cambridge,MA02139Received January2011,revision accepted May2012A B S T R A C TThe streaming potential across a porous medium is induced by a fluid flow due to anelectric double layer between a solid and a fluid.When an acoustic wave propagatesthrough a porous medium,the wave pressure generates a relative movement betweenthe solid and the fluid.The moving charge in the fluid induces an electric field andseismoelectric conversion.In order to investigate the streaming potential and theseismoelectric conversion in the same rock sample,we conduct measurements withBerea sandstone saturated by NaCl solutions with different conductivities.We mea-sure the electric voltage(streaming potential)across a cylindrical sample in NaClsolutions with different conductivities and under different pressures to determinethe DC coupling coefficients.We also measure the seismoelectric signals induced byacoustic waves with a Berea sandstone plate at different frequencies and solutionconductivities.The pressures of the acoustic waves are calibrated with a standardhydrophone(Br¨uel&Kj´œr8103)at different frequencies(15–120kHz).We calcu-late the quantitative coupling coefficients of the seismoelectric conversion at DC andat high frequencies with samples saturated by solutions with different conductivi-ties.When the Berea sandstone sample is saturated by the NaCl solution with0.32mS/m in conductivity,for example,the DC and seismoelectric coupling coefficientsat15kHz are0.024μV/Pa and0.019μV/Pa,respectively.The seismoelectric cou-pling coefficient is an important and helpful parameter for designing a seismoelectrictool.More experimental measurements of seismoelectric coupling coefficients in thefrequency range of100Hz to15kHz are needed in the future.Key words:Seismoelectric,Streaming potential,Electrolyte.I N T R O D U C T I O NWhen a porous medium is saturated with an electrolyte,an electric double layer is formed on the interface between the solid and the fluid.Some ions are absorbed into the solid sur-face and other ions remain movable in the fluid.When a seis-mic wave propagates in the fluid-saturated porous medium,∗E-mail:zhenya@ the seismic wave generates a relative movement between the solid and the fluid.The movement of the ions in the fluid forms an electric current and a seismoelectric field.When the fluid flows through a sample at a certain pressure,the fluid flow induces a current and we can measure the resultant voltage.When the fluid moves in one direction or at a low frequency,we call the voltage a streaming potential.If the fluid flow is in a high-frequency range(usually higher than 10kHz),we call it a seismoelectric voltage or AC streaming potential.688C 2012European Association of Geoscientists&EngineersMeasurements of streaming potential and seismoelectric conversion689If we can measure the pressure and the induced electric voltage,the ratio between the potential and the pressure is referred to as the voltage coupling coefficient.If the driving force is a constant pressure,we call the resulting voltage a DC streaming potential.If the driving force is a seismic or acoustic wave,we call the voltage a seismoelectric voltage.In seismoelectric conversion,the mechanical energy of a seismic wave is converted to an electric energy of an elec-tric signal in the seismoelectric conversion,which is related to many physical parameters,such as pore fluid conductivity, porosity,permeability etc.The investigation of the seismoelec-tric conversion in a formation is able to explore some of the formation parameters.In order to record the seismoelectric signals in a field or in a borehole,the conversion efficiency,or coupling efficiency,at different frequencies and conductivities, is the most important parameter for designing a seismoelectric tool to determine the source and receiver sensitivity. Theoretical studies(Pride1994;Pride and Haartsen1996; Revil and Jardani2010)show the relationship between the voltage coupling coefficient and frequency.In the low-frequency range(less than10kHz),the coupling coefficient is a constant.In the high-frequency range,the coefficient de-creases when the frequency increases.When the zeta-potential decreases with fluid conductivity,the coupling coefficient de-creases(Pride1994).Additional theoretical studies(Jardani et al.2010;Revil and Jardani2010;Revil and Florsch2010) account for the Stern layer contribution to surface conduc-tivity,to induced polarization and to complex conductivity (Leroy et al.2010).The streaming potential has been measured in laboratories in the DC and low-frequency AC(a few Hz to a few hundred Hz)range(Ahmed1964;Ishido and Mizutani1981;Mor-gan,Williams and Madden1989;Pengra,Li and Wang1999; Reppert and Morgan2002;Revil et al.2002;Zhan2009). Field seismoelectric research has been carried out at the low-to medium-frequency range(a few Hz to a few thousand Hz) in surface surveys(Thompson and Gist1993;Garambois and Dietrich2001)and boreholes(Mikhailov,Queen and Toks¨oz 2000;Hunt and Worthington2000;Singer et al.2005;Dupuis et al.2009).In recent years,high-frequency seismoelectric sig-nals(higher than10kHz)have also been recorded and anal-ysed in laboratory experiments(Zhu and Toks¨oz2005;Block and Harris2006;Zhu,Toks¨oz and Burns2008;Zhan et al. 2010;Schakel et al.2011).Since2005,more attention has been directed toward seis-moelectric measurements at high frequencies(higher than 10kHz)(Zhu and Toks¨oz2005;Zhu et al.2008).Although the seismoelectric coupling coefficient at a high-frequency range is lower than in the low-frequency range,it might be possible to apply the seismoelectric measurements to well log-ging(Dupuis et al.2009;Araji et al.2012).The frequency de-pendence of the seismoelectric coupling coefficient is related to the rock permeability,porosity,tortuosity and weighted surface to volume ratio(Johnson,Koplik and Schwartz1986; Pride1994).In this paper,DC streaming potentials are measured with Berea sandstone saturated with NaCl solutions of different conductivities.We present the laboratory set-up for quan-titative measurements of the seismoelectric voltage induced with single or multi-cycle sine bursts after the acoustic pres-sures are quantitatively calibrated.The DC streaming poten-tial coupling coefficients and high-frequency seismoelectric coupling coefficients are determined by the experimental mea-surements.R O C K S A M P L E S A N D E L E C T R O D E SA cylinder sample of Berea sandstone500is used to mea-sure the streaming potential when a fluid,with different NaCl concentrations,flows through the sample.Berea sandstones have similar compositions but have different permeability. The number500means the permeability is about500mD. Figure1(a)shows the configuration of the cylindrical sam-ple.The sample is2.54cm in diameter and2cm in length. The electrodes on the two sides of the cylinder are made with Ag/AgCl meshes.A plastic pipe seals the cylindrical surface to prevent fluid flow between the surface and the plasticpipe.Figure1Cylindrical core sample(a)and plate sample(b)with the Ag/AgCl mesh electrodes.The mesh electrode(b)with1cm diameter is mounted on the centre of the Lucite plate.C 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700690Z.Zhu and M.N.Toks¨ozFor measuring seismoelectric effects,a plate of Berea sand-stone500is immersed in a water tank.The rock plate is 15cm by15cm and2.5cm thick.It is fixed between two Lucite plates each0.25cm thick.The Ag/AgCl mesh elec-trodes are fixed in the centre of the Lucite plates(Fig.1b). The voltage between an electrode and the ground is digitally recorded.When a DC electric current goes through the two elec-trodes,which are immersed in an electrolyte(NaCl solution), the electrodes are polarized.The polarization voltage on a copper electrode can be up to0.3V.If we were to use cop-per electrodes to measure a DC voltage,the polarization of the electrodes could affect the measurements of the streaming potential.To avoid electric polarization we use a silver mesh as the electrodes to eliminate electrode polarization during the mea-surements of streaming potentials.We first soak the silver mesh in a NaCl solution,1mol/L in concentration.The silver mesh is one electrode and a steel plate is the other electrode. The electrodes are then connected to a12-volt battery.A re-sistor controls the current of100mA.A stable AgCl is formed on the surface of the silver mesh.We use the Ag/AgCl mesh as the electrode in the measurement of the streaming potentials due to its low polarization voltage(less than5mV).We also use the Ag/AgCl mesh as the electrode in the measurements of the seismoelectric signals to eliminate the possible polarization voltage.M E A S U R E M E N T S O F S T R E A M I N GP O T E N T I A L SWe measure the streaming potentials across the cylinder sam-ples saturated by NaCl solutions with different concentra-tions(100–4000ppm)and different pressures(around0.05–0.22atm)flowing through the samples.We apply a pressure difference P across the sample and measure the resulting streaming potential V.The streaming potential opposes the streaming current that flows along the pore surface and sends conduction current back through the pore volume.When the system reaches a steady state,the streaming potential V is linearly proportional to the applied pressure difference P.The proportionality constant V/ P is the streaming potential coupling coefficient Ks.We cut a10cm long cylinder of Berea sandstone500into five2-cm samples.The five samples are used for the measure-ments with the different NaCl solutions.The rock samples are saturated in a vacuum system with solutions of different NaCl concentrations for approximately3hours in orderto Figure2Experimental system for measuring streaming potential.The vertical distance between the top levels of the sample and the bottle can be changed from50–200cm.The streaming potential is mea-sured between the Ag/AgCl mesh electrodes V+and V-.The NaCl concentrations in the solutions are100ppm,500ppm,1000ppm, 2000ppm and4000ppm,respectively.form a stable electric double layer in the porous medium.We measure the streaming voltage between the electrodes V+and V-,when fluid flows through the sample in the system shown in Fig.2.The NaCl solutions have NaCl concentrations of100 ppm(0.0017mol/L),500ppm(0.0085mol/L),1000ppm (0.0171mol/L),2000ppm(0.0342mol/L)and4000ppm (0.0684mol/L),respectively.The corresponding conductivi-ties of the NaCl solutions are0.012S/m,0.048S/m,0.095 S/m,0.18S/m and0.32S/m,which are measured with a con-ductivity meter,respectively.A NaCl solution of20litres is poured into the large bot-tle shown in Fig.2.As the solution column between the top levels of the rock sample and the bottle has different vertical distances( h),we measure the voltage(streaming potential ( V))between the two sides of the sample with a digital mul-timeter(Fluke Model179).The diameter of the bottle is large enough that the vertical distance between the rock and bottle fluid surfaces is stable during the measurements.When we change the height difference( h),the water pres-sure( p)on the top surface of the rock sample can be cal-culated byρg h(ρis water density,g=9.8m/s2).At dif-ferent solution columns( h),we calculate the fluid pressure on the top surface of the rock.The DC coupling coefficient is determined by the streaming potential( V)divided by theC 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700Measurements of streaming potential and seismoelectric conversion691Figure3Typical measurement results of the streaming potential and coupling coefficient when the sample(Berea sandstone500)is saturated with distilled water as a function of pressure.vertical water pressure.Figure3shows the typical measure-ment results of the streaming potential and coupling coef-ficient at different pressures when a sample(Berea sand-stone500)is saturated with distilled water at different fluid pressures.The coupling coefficient at the NaCl concentration is de-termined by averaging the coupling coefficients at four water pressures when the heights( h)of the water columns are 50cm,100cm,150cm,and200cm,respectively.The same measurements are conducted with fluid using different NaCl concentrations.Figure4shows the DC coupling coefficients of the rock sample(Berea sandstone500)saturated with so-lutions of different NaCl conductivities.Table1shows the parameters and the measured coupling coefficients.The permeability of the rock sample is determined by mea-suring the water flowing through the sample per unit time and pressure gradient.The permeability of the Berea sandstone 500sample is about450mD.The porosity is about23%. The pH value of the solution is6.5.The room temperature is 22◦C.M E A S U R E M E N T S O F S E I S M O E L E C T R I CS I G N A L SIn order to investigate the seismoelectric conversions in the high-frequency range,we conduct seismoelectric measure-ments in a water tank.We calibrate the acoustic pressures at different frequencies.Then we record the seismoelectric waveforms and obtain the seismoelectric voltage coupling co-efficients at different frequencies.Measurement system in a water tankTo measure the seismoelectric fields induced in a rock sam-ple by an acoustic wave,we use a plate sample(Berea sand-stone500)(Fig.1b).We first saturate the porous plate with the NaCl solutions in a vacuum system.The conductivities of the NaCl solutions(0.012S/m,0.048S/m,0.095S/m, 0.18S/m and0.32S/m)are the same as those used in the measurements of the streaming potentials.The plate sample is placed in a plastic water-container35cm in length,25 cm in width and40cm in depth.This container is placed in a large water tank,100cm in length,60cm in width and 50cm in depth.This tank is large enough to eliminate the possible interference of acoustic reflection from the container walls.The measurement system(Fig.5)includes two parts:a trans-mitting and a receiving system.The transmitting system is composed of a function generator(Hewlett Packard3314A),a power amplifier(AE Techron3620)and a source hydrophone (Celesco LC-34).The receiving system includes a receiver(a hydrophone or a point electrode),a preamplifier(Olympus NDT5660C),a band-pass filter(Krohn-Hite,model3202R) and a digital oscilloscope(DATA6000).C 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700692Z.Zhu and M.N.Toks ¨ozFigure 4DC coupling coefficients of the rock sample (Berea sandstone 500)saturated with NaCl solutions of different conductivities.Table 1Parameters of NaCl solutions and measured DC couplingcoefficientNaCl NaCl Concen-trationsNaCl solution DC Couplingsolutions (ppm)(mol/L)conductivity (S/m)coefficient (μV/Pa)11000.00170.0120.325000.00850.0480.15310000.01710.0950.065420000.03420.180.035540000.06840.320.024Before we measure the acoustic pressure and seismoelec-tric voltage,we calibrate the receiving system by inputting sine waves of 0.1mV in amplitude in the frequency range of 10–120kHz.The results show the consistency of our receiv-ing and recording systems in this frequency range.The digital conversion factor of 26/μV is determined by the calibration.This factor means that an electric signal of 1μV in ampli-tude is digitally recorded by the system as 26.Therefore,the received voltage can be determined with the recorded digital waveforms.The frequency response of the acoustic receiver should be taken into account in order to measure the pressure at differentfrequencies.Figure 5The schematic diagram of the measurement sys-tem at a high-frequency range (10–120kHz)in the water container.C2012European Association of Geoscientists &Engineers,Geophysical Prospecting ,61,688–700Measurements of streaming potential and seismoelectric conversion693Figure6Schematic diagram of the calibration of the acoustic pres-sures excited by the acoustic source(LC-34)at the frequency range of10–120kHz.Calibration of the acoustic pressuresIn order to determine the seismoelectric coupling coefficient in a frequency range,first we determine quantitatively the acoustic pressures at the surface of the rock sample.Figure 6shows the set-up for the calibration.The distance between the receiver and the source is21.5cm.We use a Br¨uel& Kj´œr Type8103hydrophone(Serial No.2675790)as a standard receiver,the voltage sensitivity of which is about 26.5μV/Pa in the frequencies of10–120kHz.This hy-drophone,as a receiver,has a very good frequency response (±3dB)in a wide frequency range of4–150kHz.The manu-facturer provided the data in detail and the curve of the sensi-tivity for this hydrophone.We record the acoustic waveforms at different centre frequencies.In order to avoid the transient response of an acoustic source and to generate a stable acous-tic wave,the source is excited with an electric burst of one cycle,3-cycle and5-cycle sine waves.The received acoustic waveforms are compared.Figure7(a)shows the recorded waveforms excited with a single sine wave pulse when the centre frequency varies from 10–120kHz.The electric output of the linear power ampli-fier is fixed at about100V.Because an acoustic transducer is electronically equivalent to an electronic circle with a resister, a capacitor and an inductance,the transducer has the char-acteristic of a transient response.This is due to the transient response of the capacitor and the inductance at different fre-quencies.To avoid the transient response and the frequency shift generated with a single sine pulse,we apply a multi-cycle sine wave(3-cycle or5-cycle sine wave)to generate the acous-tic wave in the container.Figure7(b)shows a typical acoustic waveform excited by a5-cycle sine burst in the frequency range.The amplitudes of the third,fourth and fifth cycles are more stable than the first and second cycles,which are af-fected by the transient response.The acoustic amplitudes are determined by averaging the amplitudes of the third,fourth and fifth cycles in5-cycle measurements.The acoustic pressure between the Lucite plates(Fig.6) can be determined from the recorded acoustic amplitudes and the receiver sensitivity provided by the manufacturer at the frequency range.Figure8shows the acoustic pressures gener-ated by the acoustic source at the frequency range of10–120 kHz.The centre frequency of the source hydrophone is about 70kHz.In the low-frequency range(<70kHz)the pressure decreases faster than in the high-frequency range(>70kHz). Some previous measurements(Pengra et al.1999;Deck-man,Herbolzheimer and Kushnick2005)were conducted with a continuous sine wave in a small container at low fre-quencies.Because the continuous sine wave forms a standing wave formed by the forgoing and reflecting waves in a limited container,the acoustic amplitude dramatically varies with the frequency and the location between the source and receiver. It is very difficult to determine the acoustic pressure at the location of the rock sample using a continuous sine signal. Therefore,we use a‘pulse’method to avoid the complexity and use a multi-cycle sine wave burst to avoid the transient response of the hydrophones.Measurements of seismoelectric signalsBefore we measure the seismoelectric signals,we put the rock sample in distilled water for one hour and then dry the sample in the air for more than16hours.After the sample is dried,it is placed in a sealed container and vacuumed by a mechanical vacuum pump for more than two hours.We conduct an independent seismoelectric measurement to determine the voltage variation with the saturated time.We keep the same acoustic pressure and measure the seismoelec-tric voltage every20minutes after the rock sample is satu-rated.The measured voltage increases at the beginning and then the voltage becomes stable about3hours later.Based on this experiment,we start the measurements after three hours when the rock samples are saturated in a vacuum system.The measurement usually takes about half a day for each fluid of a given conductivity.Before we measure the seismoelectric signals we conduct a test measurement to confirm that the recorded signal is a seismoelectric signal.C 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700694Z.Zhu and M.N.Toks ¨ozFigure 7Typical acoustic waveforms received with the hydrophone (Br ¨uel &Kj´œr 8103)when the source (LC-34)is excited with 1-cycle (a)or 5-cycle (b)sine burst.The amplitudes of the acoustic waveforms are normalized with 20mV.We set up a measurement system,using a tap-water con-tainer similar to that shown in Fig.5and move the elec-trode,located on the front of the Lucite plate,1cm/trace closer to the source.When the rock sample is removed from the water tank,we measure the electric signals induced by a 70-kHz single acoustic pulse and recorded with the electrode.Figure 9(a)shows the background noise of the measurement system.The strong noise at the beginning (<0.05ms)is theC2012European Association of Geoscientists &Engineers,Geophysical Prospecting ,61,688–700Measurements of streaming potential and seismoelectric conversion695Figure8The acoustic pressures of the acoustic field measured at the position shown in Fig.6and generated by the acoustic source(LC-34)in the frequency range of10–120kHz.EM wave radiated by the electric source,because it is im-possible to completely shield the receiver.There is no visible electric signal when the acoustic wave arrives at the electrode (around0.15ms).This rules out the possibility that the elec-trode vibration induces an electric signal.When we put the rock sample back into the water tank and repeat the measurements to record the electric signals shown in Fig.9(b)and compare the signals with the back-ground signals(Fig.9a),we confirm that the acoustic wave induces a radiating seismoelectric wave(around0.15ms)at the interface between the rock sample and the water due to seismoelectric conversion.This is based on the propagation time of the acoustic wave from the source transducer to the sample.When an acoustic wave propagates in a homogeneous porous medium saturated with fluid,a stationary or localized seismoelectric field can be induced inside the medium.The apparent velocity of the seismoelectric field is the velocity of the acoustic wave.It is referred to as a coseismic seismoelec-tric field.If there is a discontinuous interface or an inter-face between two media,the induced seismoelectric field is a radiating electromagnetic(EM)boratory experi-ments(Zhu and Toks¨oz2003,2005)measured this EM wave induced at a fracture.We measure the electric signals received by the electrode V+,as shown in Fig.5and record the electric waveforms.Figure10shows the typical electric signals induced by5-cycle (Fig.10a)and3-cycle(Fig.10b)sine bursts for the Berea sandstone500sample saturated with the NaCl solution of 100ppm concentration.The amplitudes are normalized by 0.02mV in Fig.10.For each NaCl solution,we record the electric signals in-duced by a single or multi-cycle sine waves in the frequency range of10–120kHz.The recorded amplitudes of the seismo-electric signals can be converted to voltage using the conver-sion factor of the receiving system.In our system,the recorded value of26is equivalent to1μV on the electrode V+.D A T A P R O CE S S I N GWe calculate the streaming potential and the seismoelectric voltage at the DC fluid flow and at the high-frequency range from the above experimental measurements,respectively.The coupling coefficient at the DC fluid flow is obtained by the voltage measured in the experiments divided by the pressure based on the water height above the sample.The seismoelectric voltage coupling coefficients Ks can be calculated by the amplitude of the electric signals divided by the acoustic pressure at each frequencyω:Ks(ω)=V+(ω)P(ω),(1)C 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700696Z.Zhu and M.N.Toks ¨ozFigure 9The electric signals induced by a 70-kHz single acoustic pulse in a tap-water tank without the rock sample (Fig.9a)and with the rocksample (Fig.9b)when the front electrode moves closer to the acoustic source by a 1cm/trace.where V +(ω)is the amplitude of the electric signal recorded with electrode V +at the frequency ωand P (ω)is the acous-tic pressures measured with the standard hydrophone at the sample position (Fig.8).Figure 11shows the voltage coupling coefficients of Berea sandstone 500saturated by NaCl solutions with the conduc-tivity of 0.012S/m,0.048S/m,0.098S/m,0.18S/m and 0.32S/m as a function of frequency on a linear scale.At aC2012European Association of Geoscientists &Engineers,Geophysical Prospecting ,61,688–700Measurements of streaming potential and seismoelectric conversion697Figure10Typical electric signals induced by5-cycle(a)and3-cycle(b)sine bursts and measured by the electrodes V+with the Berea sandstone 500samples saturated with a NaCl solution of100ppm concentration.The amplitudes of the electric waveforms are normalized with20μV.low-frequency range(<40kHz),the measurements show the same unusual variations.These are most likely due to the interference of disturbed acoustic waves with those re-flected from the side of the tank.In order to improve the measurement at low frequencies,a bigger water tank is needed to separate the noise and the signal in a time domain.When the concentration of the solution is0.0684mol/L (0.32S/m in conductivity),the maximum coupling coefficient at10kHz is about0.019μV/Pa.This coupling coefficientC 2012European Association of Geoscientists&Engineers,Geophysical Prospecting,61,688–700698Z.Zhu and M.N.Toks ¨ozFigure 11The seismoelectric voltage coupling coefficients measured at the frequency range of 10–120kHz with Berea sandstone 500saturatedby NaCl solutions with different conductivities.is slightly higher than the 0.016μV/Pa measured by Pengra et al .(1999)with the higher solution concentration of 0.1mol/L at very low frequencies (<20Hz).Figure 12shows the DC coupling coefficients and the seis-moelectric voltage coupling coefficients at high frequencies in a log scale when the Berea sandstone 500samples are satu-rated with the NaCl solution of the different concentrations.When the conductivity of the NaCl solution increases,the cou-pling coefficient decreases.In the high-frequency range,the coupling coefficient decreases when the frequency increases.At the lowest frequency (15kHz),the measured coupling coefficient is lower than but close to the DC coupling coeffi-cient.This means the coupling coefficient has a small change from DC to the high-frequency (about 15kHz).Our experi-mental facility is limited by the transducer’s frequency range and the size of the water tank;we could not conduct the seis-moelectric measurements at frequency ranges of lower than 10kHz.More measurements in the frequency range from hundreds Hz to 10kHz are needed.C O N C L U S I O N SWhen a fluid flows through a porous rock or an acoustic wave generates fluid flow in a porous rock,moving charges inducean electric field that originates from the electric double layer.We measured the DC streaming potentials and seismoelectric voltage coupling coefficients in high frequencies (10–120kHz)with samples of Berea sandstone 500.The DC voltages measured when the NaCl solutions with conductivities between 0.012–0.32S/m flowed through a cylindrical sample were used to determine the DC coupling coefficients.The values were between 0.3–0.024μV/Pa.The results compare well to other measurements (Pengra et al .1999).We first investigated the acoustic fields generated by a single sine pulse,a continuous sine wave and multi-cycle sine bursts in the water tank,respectively.Then we conducted electric and acoustic calibrations for the receiving part of our mea-surement system in order to measure the seismoelectric cou-pling coefficient at high frequencies (10–120kHz).Based on the frequency response of the Br ¨uel &Kj´œr 8103hydrophone provided by the manufacturer,we used the multi-cycle sine burst to measure the acoustic pressures at the different fre-quencies.We measured the seismoelectric voltage induced at the rock surface when the sample was saturated by the differ-ent NaCl solutions.The experimental results show that the seismoelectric volt-age coupling coefficient decreases when the fluid conductivityC2012European Association of Geoscientists &Engineers,Geophysical Prospecting ,61,688–700。

基于ABAQUS的水下爆炸计算仿真实例

Modeling Submerged Structures Loaded byUnderwater Explosions with ABAQUS/ExplicitDavid B. WoyakABAQUS Solutions Northeast, LLCAbstract: Finite element analysis can be used to predict the transient response of submergedstructures that are externally loaded by an acoustic pressure shock wave resulting from anUnderwater Explosion (UNDEX). This class of problem is characterized by a strong couplingbetween the structural motions and acoustic pressures at the fluid-structure wetted interface. The structural behavior is a combination of long time (low frequency) response dominated by anadded mass effect, short time (high frequency) response dominated by radiation damping, and intermediate time-frequency response where both added mass and radiation damping behaviorare present. For the finite element method to be useful, the analyst must develop modelingtechniques and procedures that yield accurate and computationally tractable solutions. Modeling procedures and guidelines were developed for use with an explicit dynamics code that offersadvanced features such as: pressure formulated acoustic elements, surface based fluid-structure coupling, surface based absorbing (radiation) boundaries, and automated incident wave loadingfor the fluid-structure wetted interface. The modeling guidelines address issues such as: locationof the fluid acoustic domain outer boundary, meshing of the acoustic domain, representation ofthe shock wave, and solution efficiency. These modeling procedures and guidelines aredemonstrated with an ABAQUS/Explicit analysis of an UNDEX experiment in which a submergedtest cylinder was exposed to a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993).General BackgroundABAQUS/Explicit is an efficient tool for simulating the transient response of structural-acoustic systems, of which the response of submerged structures loaded by acoustic shock waves resultingfrom an Underwater Explosion (UNDEX) is an important problem class. This paper provides abrief discussion on the general nature of the structural-acoustic interaction and describes modeling studies that address general Finite Element Analysis (FEA) requirements for the accuratesimulation of UNDEX problems. The studies described in this report have general application to awide range of structural-acoustic problems, not just the analysis of submerged structures. Anexample analysis of a submerged cylinder is used to illustrate an UNDEX problem.UNDEX analyses can be generally characterized as transient simulations of acoustic scattering behavior. However, the objective of an UNDEX analysis is to evaluate the response of thesubmerged structure and not necessarily the acoustic response. The finite element model for the external acoustic domain must be adequate to represent the influence of the water on the structural response. The discussion herein will be restricted to those cases where the external fluid behavesas a linear acoustic fluid with no cavitation. Therefore, the model of the external acoustic domainneed only be tailored to provide an accurate loading on the structure and does not need toaccurately represent the acoustic waves that will travel away from the structure. It should be noted2002 ABAQUS Users’ Conference1that procedures for UNDEX analyses which include fluid cavitation will be available inABAQUS/Explicit with the release of Version 6.3 (Prasad & Cipolla, 2001).The total acoustic pressure in the external fluid that results from an underwater explosion consistsof the known incident shock wave (incoming) pressure and the unknown scattered wave(outgoing) pressure. The scattered wave pressure consists of two parts, a reflected part that is associated with the shock wave interacting with an ideal rigid, immovable structure and avibratory part that results from the motions of the structure at the interface with the fluid. When cavitation is not present, it is desirable to let the external acoustic domain represent only thescattered portion of the total acoustic pressure. The shock wave incident pressure load is applieddirectly to the structural mesh at the fluid-structure wetted interface. Acoustic loads associatedwith the reflected part of the scattered pressure are applied to the fluid mesh at the wettedinterface. The full scattered pressure (reflected and vibratory) is obtained as the solution for theacoustic element pressure degrees of freedom, and the complete scattered pressure loading on the structure is generated through the fluid-structure coupling equations. The acoustic loads are a characteristic of the incident shock wave, and are obtained from the fluid particle accelerations ina direction normal to the surface that defines the fluid-structure wetted interface.In the discussion that follows the capability of ABAQUS/Explicit to efficiently perform UNDEX analyses is demonstrated. The ABAQUS features utilized in solving this class of problem are:1. Computationally efficient pressure based acoustic elements.2. Surface based automated acoustic-structure coupling.3. Acoustic-structure coupling for mis-matched meshes.4. Surface based impedance models for representing non-reflecting fluid boundaries.5. Automated shock wave loading at the fluid-structure interface.Acoustic Domain Outer BoundaryUNDEX problems are characterized by a strong coupling between the structural motions and acoustic pressures at the wetted interface. The system response in a strongly coupled structural-acoustic system can be described as being a combination of the following types of response:1. Late Time - Low Frequency: Characterized by structural wavelengths that aresignificantly shorter than the associated acoustic wavelengths. The effect of the externalfluid on the structure is that of adding an effective mass to the structure on the wettedinterface. The scattered energy within the acoustic domain remains near the structurewith very little energy radiating away from the structure.2. Early Time - High Frequency: Characterized by structural wavelengths that aresignificantly longer than the associated acoustic wavelengths. The effect of the externalfluid on the structure is to act as a simple radiation damper at the wetted interface. Mostof the scattered energy within the acoustic domain radiates away from the structure.3. Intermediate Time - Frequency: Characterized by structural wavelengths that are ofsimilar length compared to the associated acoustic wavelengths. The effect of the2002 ABAQUS Users’ Conference 2external fluid on the structure is that of adding both effective mass and damping to thestructure. Comparable levels of scattered energy remain near the structure and areradiated away from the structure.Due to the high density and bulk modulus of water the finite element model for an UNDEXanalysis must be capable of accurately simulating all three ranges of structural-acoustic response.It should be noted that for some other types of structural-acoustic analyses, where the fluid is verylight compared to the structure, not all response types may be of equal importance. For example,the added mass effect of air acting upon heavy structures is often of no consequence.The acoustic model for the outer boundary of the external fluid domain must provide adequatenon-reflecting behavior over all three time-frequency ranges. Non-reflecting outer boundarymodels are implemented in ABAQUS/Explicit (Version 6.2) via a surface based boundary impedance. ABAQUS has several imbedded surface impedance models, of which the circular and sphere types were used for analyses described herein. These impedance models are based upon the classical solutions for a 3-dimensional point source (sphere) and a 2-dimensional point source or3-dimensioanl linear source (circular). The default impedance model corresponds to a simpleplane wave radiation condition, which is well suit to simple acoustic tube test simulations.For the late time - low frequency response range, the extent of fluid contributing to the added massis largest for the longest structural response wavelength. Also, for the early time - high frequency response range, the longest structural response wavelength has the potential to generate efficient radiating acoustic waves with the longest wavelengths. Therefore, the location of the fluid meshouter boundary can be based upon the structure’s longest characteristic response wavelength. Ageneral guideline for locating the acoustic mesh outer boundary was developed by performing aseries of analyses representing the harmonic translational motion of a rigid infinite cylinder in aninfinite fluid domain. This type of motion is closely related to the transverse motion of a cylindersection for beam bending response modes. A 2-dimensional rigid cylinder cross section (10”radius) was placed within a circular fluid domain, for which the outer boundary was located at 2,3, and 4 cylinder radii. The fluid was water with a bulk modulus of 345,600 psi and a sound speedof 60,000 inches per second. ABAQUS/Explicit was used to drive the cylinder with a harmonicmotion until steady state conditions were achieved. Baseline analyses with very refined acousticmeshes were used to represent the exact solutions. The baseline analyses utilized linear acoustictriangle elements with approximately 42 element divisions per acoustic wavelength. The outer boundary for the baseline analyses was located two full acoustic wavelengths away from thestructure, and utilized the circular type impedance boundary. The boundary evaluation modelshad a minimum of 20 element divisions per acoustic wavelength for the highest driving frequency,and the maximum acoustic element size was set at 1.5 inches for the lowest driving frequencies.Figure 1 shows the baseline results for the complex radiation impedance of the driven cylinder(force/velocity). The impedance values are plotted against the ratio of the structural wavelength,which is the cylinder circumference, to the driving frequency acoustic wavelength. The radiation reactance (imaginary) represents an added-mass effect and the radiation resistance (real)represents the acoustic damping. Figure 1 clearly shows all three time-frequency response ranges,with the radiation impedance transitioning from added mass at low frequencies to radiationdamping at high frequencies. Figure 2 shows a plot of the error ratio for the radiation impedance predictions with the evaluation models. The radial thickness of the fluid mesh for the outerboundary at 2, 3 and 4 cylinder radii, corresponds to approximately 1/6, 1/3, and 1/2 of thestructural wavelength. Setting the boundary at 2 cylinder radii (1/6 structural wavelength) works2002 ABAQUS Users’ Conference3well at high frequencies but can introduce significant error in the added mass at low frequencies.The error oscillations within the 5% error range at the higher driving frequencies appear to be dueto the outer boundary being placed near integer multiples of half the acoustic wavelength. Placingthe outer boundary so that the fluid domain thickness is between 1/3 and 1/2 the largest structural wavelength provides for reasonable accuracy when using a sound source based outer boundarysurface impedance model. The performance when using a classical plane wave boundary conditionis significantly diminished, and would require at least doubling the extent of the fluid domain.Fluid Mesh Requirements for Representing the Shock WaveThe classical representation of a spherical shock wave associated with UNDEX loading is characterized by an instantaneous pressure rise to a peak value followed by an exponential decay.An UNDEX analysis in which the external fluid is modeled with finite elements cannot accurately represent a shock wave having an instantaneous pressure rise because the infinite pressure gradientat the shock front implies infinite fluid particle acceleration, so that the acoustic loads associatedwith the reflected part of the scattered pressure become indeterminate. Therefore, the shock frontmust be modeled such that the pressure rise occurs over a period of time, designated the “risetime”. A reasonable value for the rise time can usually be obtained from experimental oranecdotal data. The pressure vs. time history of the shock wave at a known distance form thesource can be used to evaluate element size requirements for the acoustic mesh. This isaccomplished by means of a simple acoustic tube evaluation model.A simple acoustic tube model was constructed with the linear tetrahedron acoustic elements thatwill be used in the subsequent UNDEX example analyses. Acoustic loads representative of aplanar shock wave are applied at one end of the model with the ABAQUS incident wave loading capability. The end at which the loads are applied represents a rigid immovable wall. Theresulting reflected wave travels down the acoustic tube. A simple plane wave absorbing boundarycan be applied to the opposite end of the tube, or the tube can be made of sufficient length so thatthe test analysis finishes before the reflected wave reaches the opposite end.Figure 3 shows the results for a tube analysis in which the nominal element size is equal to 1.5times the wave propagation distance corresponding to the rise time of the shock front. The onlyoutput quantity of concern in these acoustic tube analyses is the pressure at the rigid wall(scattered pressure). An ideal solution for this problem would have the reflected wave being anexact copy of the shock wave. This is clearly not the case for the Figure 3 model. Figure 4 isanother analysis with the element size set at 1/4 the rise time propagation distance. The scattered pressure matches the shock pulse very well. However, there is still a fair degree of oscillation inthe early time solution. It should be noted that the range in the pressure oscillations can become noticeably less when using brick type acoustic elements.Figure 5 shows some additional solutions with the element size set at 1.5 times the rise timedistance, for which the time increment was varied via direct user control. As the time increment is reduced the mean response approaches that of the incident shock wave. This illustrates howsimple acoustic tube models can also be used to evaluate the time increment requirements foraccurately representing the reflected wave loading. Figure 5 also suggests that a relatively coarsefluid mesh may provide sufficient solution accuracy for the structural response as long as thestructure being analyzed responds at low frequencies relative to the reflected wave oscillations.For these cases, the pressure impulse (time integral of pressure) associated with the reflected and2002 ABAQUS Users’ Conference 4incident shock waves should have relatively good correlation. Figure 6 shows the pressure impulse curves generated from the Figure 5 analyses, and suggests that using a time increment that is lessthan or equal to 1/20 of the rise time may provide good results with the coarse acoustic mesh for alow frequency structural system.Example Problem DescriptionThe UNDEX example problem is based upon an experiment in which a submerged test cylinderwas exposed to a shock wave produced by a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993). The test cylinder is made of T6061-T6 aluminum, has an overall length of 1.067 meters, an outside diameter of 0.305 meters, a wall thickness of 6.35 millimeters and welded endcaps that are24.5 millimeters thick. The cylinder was suspended horizontally in a 40-meter deep fresh watertest quarry (sound speed =1463 meters/second). The 60-pound HBX-1 explosive charge and the cylinder were both placed at a depth of 3.66 meters, with the charge centered off the side of thecylinder and located 7.62 meters from the cylinder surface. The suspension depths, charge offsetand duration of the test were selected such that cavitation of the fluid would not be significant andno bubble pulse would occur. During the UNDEX test, two pressure transducers were positioned7.62 meters from the charge, away from the cylinder, but at the same depth as the cylinder. These transducers provided an experimental determination for the pressure vs. time history of theincident spherical shock wave as it traveled by the point on the cylinder closest to the charge.Figure 7 is a time history of the recorded shock wave pressure used as input to theABAQUS/Explicit analyses. Strain gages were placed at several locations on the outer surface ofthe test cylinder, as shown in Figure 8. The strain gage experimental data was filtered at 2000 Hz,with the experimental data presented herein obtained by digitizing the published Kwon & Foxstrain data.ABAQUS/Explicit Model & ResultsThe test cylinder was meshed with 2400 S4R finite strain shell elements and contained 2402 nodes (14412 dof) on 40 circumferential and 53 axial element divisions. The element connectivity issuch that each shell normal is directed into the external fluid. The shell element nodes arepositioned on the outside surface of the test cylinder. The cylinder body elements directlyadjacent to the endcaps have reduced mass & stiffness and are only used to provide a surface that corresponds to the thickness of the endcaps. BEAM type MPCs are used to rigidly tie theendcaps to the main cylinder body.The external fluid is meshed with 4-noded AC3D4 acoustic tetrahedral elements. The outerboundary of the external fluid is represented by cylindrical and spherical surfaces with theappropriate surface impedance absorbing conditions. The characteristic radius of the fluid outer boundary is set at 3 shell radii, thus the thickness of fluid modeled about the cylinder represents approximately 1/3 of the cylinder’s outer circumference (rigid body translational wavelength).Based upon the mesh boundary study this location should be sufficient to provide reasonablyaccurate results. Figure 9 shows the cylinder and first acoustic mesh that was used in the analysis,with the top half of fluid removed for clarity. The shock wave rise time is 0.0182 milliseconds, corresponding to a wave propagation distance of 0.0266 meters. The nominal element size at thewetted interface is also set at 0.0266 meters and increases in size to a nominal 0.080 meters at the2002 ABAQUS Users’ Conference5outer fluid boundary. An acoustic element size of 0.080 meters corresponds to approximately 12 element divisions per acoustic wavelength for a 1500 Hz response. Figure 10 provides the resultsof the acoustic tube validation for this degree of mesh refinement. Acoustic Mesh #1 contains39186 elements and 7947 pressure degrees of freedom. Figure 11 shows the second acousticmesh that was used in the analysis, with the top half of fluid removed for clarity. The nominalelement size at the wetted interface is set at 0.010 meters and increases in size to a nominal 0.030meters at the outer fluid boundary. Figure 12 provides the results of the acoustic tube validation corresponding to acoustic Mesh #2, which contains 463114 elements and 87745 pressure degreesof freedom.Figure 13 shows the ABAQUS predicted axial strain response at strain gage location B1 whenusing the coarse (#1) and refined (#2) acoustic meshes. The response curves are very close both in magnitude and phasing. The close correlation between the two analyses was also apparent at theother strain gage locations. This indicates that for the applied UNDEX loading the structuralresponse times are long when compared to the reflected wave oscillations obtained in the acoustictube validation analyses. This result was predictable when considering an eigenvalue analysis forthe cylinder with no external fluid. The modes that have the greatest potential for producingdamage have frequencies well below 1500 Hz, and will be further reduced when the cylinder is submerged due to the added mass effect. The cylinder modes have response periods that are significantly longer than the shock wave rise time or reflected wave pressure oscillations. Thus,for this particular example, using an acoustic mesh and solution time increment that reasonablycaptures the shock wave reflected pulse and can represent the scattered acoustic waves at thestructural response frequencies is adequate for obtaining a good solution.The response shown in Figure 13 is dominated by the fundamental beam bending mode of thecylinder, for which the dominant motion is transverse to the cylinder axis. At any point along the cylinder axis the motion is dominated by a translation of the cross section through the fluid,similar to the motion used in the infinite cylinder modeling study. The only damping mechanismsin the analyses were due to acoustic radiation and the /Explicit default values for element bulk viscosity. The acoustic model does not include any losses due to hydrodynamic drag (fluidviscosity) associated with the motions of the cylinder. The effect of hydrodynamic drag on thelate time response of the cylinder is clearly shown in Figure 14, where the predicted axial strain response is compared to the experimental data. The experimental data was digitized from apublished curve (Kwon & Fox, 1993), and was shifted by 0.2 milliseconds in order to align the experimental and analysis time axes. The solution designated as ALPHA = 0, represents theoriginal analysis, whereas the analysis designated as ALPHA=750 utilized mass proportionaldamping (10% critical at 600 Hz) applied to the cylinder as an approximation for the effects of hydrodynamic drag. The application of ALPHA damping does not have an adverse effect on thesolution critical time increment. ALPHA damping does not significantly affect the early timeresponse (high frequency), but does significantly reduce the late time response (low frequency).This is consistent with what is observed with the experimental data. In any event, ignoring hydrodynamic drag in an UNDEX analysis will produce conservative (high) levels for thestructural response, which is often a desirable trait when doing a design evaluation analysis.Figure 15 shows the levels of Accumulated Plastic Strain (PEEQ) on the outer surface of the shellat the end of the analysis with fluid Mesh #1 and ALPHA= 750. No change occurs in the peakplastic strain level of the cylinder wall after the first 0.34 milliseconds. Recalling that the entireshock pulse duration is 2.0 milliseconds, this truly is an early time response. No change occurs inthe peak accumulated plastic strain of the endcaps after 2.84 milliseconds, which indicates that the2002 ABAQUS Users’ Conference 6endcap response may be influenced to a greater extent by the late time response. Unfortunately,there were no strain gages attached to the endcaps and the cylinder wall gages located in theregions of high plastic strain failed during the test. Table 1 compares the peak accumulated plasticstrains obtained with the two acoustic meshes, with and without ALPHA damping. The results comparison between Mesh #1 and Mesh #2 is very good. The effect of ALPHA damping on thecylinder wall PEEQ is very small, but is significant for the endcap response. Table 1 also providesa comparison of the solution times for the analyses, and illustrates the solution efficiency of theacoustic elements as compares to structural elements.ConclusionsABAQUS/Explicit provides an efficient means to evaluate the transient response of structural-acoustic systems loaded by external acoustic sources. This was illustrated with the analysis of a submerged cylinder acted upon by a shock wave generated by an underwater explosion. Themodeling studies presented in this paper indicate that sufficient accuracy for a submergedstructure’s response can be obtained when positioning the external absorbing boundary of theacoustic domain a distance from the structure of between 1/3 to 1/2 the longest characteristicstructural wavelength. Modeling studies also indicated that the degree of refinement in theacoustic domain mesh can be tailored to the characteristics of the shock pulse and the nature of structural response, i.e., short vs. long response times as compared to the shock pulse transient.Table 1. Model statistics and results comparisons.Item Cylinder Only Acoustic Mesh #1 Acoustic Mesh #2 No. Acoustic Elements N/A 39186 463114No. Acoustic DOF N/A 7947 87745No. Shell Elements 2400 2400 2400No. Shell DOF 14412 14412 14412Solution Time Increments 4730 4730 13873CPU Time (Seconds) 281 426 4590CPU per Increment 0.059 0.090 0.331PEEQ Cylinder Wall(Alpha = 750) N/A 0.00820 0.00810PEEQ Cylinder Wall(Alpha = 0) N/A 0.00838 0.00828PEEQ Endcap Center(Alpha = 750) N/A 0.00626 0.00611PEEQ Endcap Center(Alpha = 0) N/A 0.01007 0.009852002 ABAQUS Users’ Conference78 2002 ABAQUS Users’ ConferenceFigure 1. Baseline radiation impedance results for an infinite rigid cylinder.Figure 2. Error ratio for the radiation impedance evaluation models.2002 ABAQUS Users’ Conference 9Figure 3. Acoustic tube with elements 1-½ the rise time propagation distance.Figure 4. Acoustic tube with elements ¼ the rise time propagation distance.10 2002 ABAQUS Users’ ConferenceFigure 5. Additional results for 1-½ rise time element mesh.Figure 6. Pressure impulse curves from Figure 5 analyses.Figure 7. Incident shock wave pressure transient.Figure 8. Test Cylinder Strain Gage Locations.2002 ABAQUS Users’ Conference11Figure 9. Cylinder and acoustic Mesh #1.Figure 10. Acoustic tube validation results for Mesh #1. 12 2002 ABAQUS Users’ ConferenceFigure 11. Cylinder and acoustic Mesh #2.Figure 12. Acoustic tube validation results for Mesh #2. 2002 ABAQUS Users’ Conference 13Figure 13. Axial strain response at gage location B1.Figure 14. Comparison plots of response at strain gage B1.142002 ABAQUS Users’ ConferenceFigure 15. Accumulated plastic strain in the test cylinder.References1. Kwon, Y.W. and P.K. Fox, “Underwater Shock Response of a Cylinder Subjected to a SideOn Explosion,” Computers and Structures, Vol. 48, No. 4, 1993. 2. Prasad, B.R. Nimmagadda and J. Cipolla, “A Pressure Based Cavitation Model for Underwater Shock Problems,” Shock and Vibration Symposium, Paper U30, November, 2001.2002 ABAQUS Users’ Conference15。

Superluminal behavior and the Minkowski space-time

a r X i v :g r -q c /0603024v 1 8 M a r 2006Superluminal behavior and the Minkowski space-timeDaniela Mugnai ∗Nello Carrara”Institute of Applied Physics,CNR Florence Research Area,Via Madonna del Piano 10,50019Sesto Fiorentino (FI),ItalyBessel X-waves,or Bessel beams,have been extensively studied in last years,especially with regard to the topic of superluminality in the propagation of a signal.However,in spite of many eﬀorts devoted to this subject,no deﬁnite answer has been found,mainly for lack of an exact deﬁnition of signal velocity.The purpose of the present work is to investigate the ﬁeld of existence of Bessel beams in order to overcome the speciﬁc question related to the deﬁnition of signal velocity.Quite surprisingly,this ﬁeld of existence can be represented in the Minkowski space-time by a Super-Light Cone which wraps itself around the well-known Light Cone.The propagation of Bessel X-waves has been extensively analyzed in last years,especially with regard to the topic of superluminality in connection to the signal propagation.Many contributions were devoted to this topic,both from a theoretical and experimental point of view [1,2,3,4,5,6].Bessel X-waves,which are also known as Bessel beams,belong to the class of localized waves.The peculiarity of this type of waves is that they are well localized in space,unlike a “usual”wave which occupies the entire space.As is well known,a u B Bessel beam is the result of superimposing an inﬁnite number of plane waves,each of them with a direction of propagation tilted by the same angle θ0with respect to a given axis,say z.In cylindrical coordinates (ρ,z,ψ),the beam is given by u B (ρ,z,t )=J 0(k 0ρsin θ0)exp [ik 0z cos θ0]exp(−iωt )(1)where k 0=ω/c is the wavenumber in the vacuum,and ωis the frequency of the beam.Function J 0denotes the zero-order Bessel function of ﬁrst kind,which,apart from inessential factors,can be written as [7]J 0(x )= π0exp(ix cos ϕ)dϕ.(2)The characteristic features of a Bessel beam are that it supplies well-localized energy,that propagates along the z-axis with no deformation in its amplitude [8,9],and that both phase and group velocities are greater than the light velocity c [2,3].A U B Bessel pulse limited in time,which is the theoretical deﬁnition of signal,can be obtained by superimposingan inﬁnite number of frequencies.After integration of Eq.(1)over dω,and by substituting the Bessel function J 0with its integral form,we obtainU B (ρ,z,t )=π0δ ρc sin θ0−t dϕ,(3)which is diﬀerent from zero only ift ≤ 1∗E-mail:d.mugnai@r.it-6-4-20246-6-4-20246z tFIG.1:Bessel beam velocities for three diﬀerent values of parameter θ0,in the z −t plane,for ρ=0(Euclidean space).The red line indicates light velocity c (for θ0=0)taken here as equal to 1.Green,pink,and blue lines represent the beam velocities for θ0=20◦,30◦,and 40◦,respectively.For ρ=0,the intersection point changes its position with no modiﬁcation in the line behavior.bFIG.2:Schematic representation of the Super-Light Cone in the Minkowski space-time (pseudo-Euclidean space).The green zone represents the Light-Cone,while the blue zone around it is the ﬁeld of existence of the Bessel beam.Quantity v b is the beam velocity for a given axicon angle,θ0.For θ0=0,the beam is reduced to a plane wave,and its velocity then becomes equal to c .In this situation,the ﬁeld of existence of the beam goes to zero,the Super-Light Cone narrows and becomes equal to the Light-Cone.Since the Bessel pulse propagates along the z-axis,we can deduce that the motion of the beam in the z −t plane (see Fig.1)is within a conical surface similar to the Light Cone,where light velocity c is replaced by velocity v b =c/cos θ0,and t is a real quantity:we can say that the propagation of a Bessel pulse in the Euclidean-space corresponds to a Super-Light Cone in the pseudo-Euclidean space-time of Minkowski.In other words,by introducing a second spatial coordinate,for a given value of θ0,we obtain a Super-Light Cone like the one of Fig.2,where straight line v b ,which depends on θ0,is the beam velocity.For θ0=θmax ,v b represents the border line which determines the existence of the ﬁeld:the Bessel beam exists only in the blue zone.Inside this cone of existence,the past Super-Light Cone,t <0,represents the time interval prior to generation of the beam.The beam originates at t =0,and for t >0(future Super-Light Cone)propagates along the z axis with velocity v b (blue line,in Fig.2).For θ0=0the beam reduces to a plane wave,its velocity becomes equal to c (green line,in Fig.2),and the Super-Light Cone becomes the Light Cone (green cone in Fig.2).Now,since Bessel beams are real quantities (they have been experimentally generated and measured),and since Eq.(1)is capable of describing the scalar ﬁeld of the beam as being due to a speciﬁc experimental set-up [10],we canconclude that the Super-Light Cone places a new upper speed limit for all objects.Massless particles can travel not only along the Light Cone,but also along the Super-Light Cone in the region between the Super-Cone and the Cone, while the world-lines remain conﬁned within the Light-Cone.In substance,we can think that c is the velocity of light in its simplest manifestation(wave),while more complex electromagnetic phenomena,such as the interference among an inﬁnite number of waves,may originate diﬀerent velocities.The maximum valueθmax of axicon angleθ0sets the maximum value of the beam velocity.Since theﬁled depth,that is,the spatial range in which the beam exists,is proportional to tanθ−10,θ0can never reach the value ofπ/2.If it were possible to obtain values ofθ0close toπ/2, we should have almost immediate propagation in a nearly-zero space,rather like an ultra fast shot destined to slow down immediately.The change in the upper limit of the light velocity(the Bessel beam is“light”)does not modify the fundamental principles of relativity and the principle of causality,as demonstrated by recent theory dealing with new geometrical structure of space-time[11].The principle that“the speed of light is the same for all inertial observers,regardless of the motion of the source”,remains unchanged,provided that the substitution c−→v b(=c/cosθ0)is made in the Lorentz transformations.In this way,the direction of the beam-light does not depend on the motion of the source, and all observers measure the same speed(v b)in all directions,independently of their motions.[1]P.Saari and K.Reivelt,Phys.Rev.Lett.79,4135(1997).[2]D.Mugnai,A.Ranfagni,and R.Ruggeri,Phys.Rev.Lett.84,4830(2000).[3]I.Alexeev,K.Y.Kim,and chberg,Phys.Rev.Lett.88,073901(2002).[4]Ioannis M.Besieris and Amr M.Shaarawi,Optics Express12,3848(2004).[5]Miche Zamboni-Rached,Amr M.Shaarawi,and Erasmo Recami,J.Opt.Soc.Am.A21,1564(2004).[6]Peeter Saari and Kaido Reivelt,Phys.Rev.E69,036612(2004)[7]M.Abramowitz and Irene A.Stegun,Handbook of Mathematical Functions,Dover Pub.,New York,1970,p.360,n.9.1.21.[8]J.Durnin,J.J.Miceli,and J.H.Eberly,Phys.Rev.Lett.58,1499(1987).[9]P.Sprangle and B.Haﬁzi,Phys.Rev.Lett.66,837(1991);J.Durnin,J.J Miceli,and J.H.Eberly,Phys.Rev.Lett.66,838(1991).[10]By means of a vectorial treatment,it was prouved that the scalarﬁeld of Eq.(1)is that of a beam as produced by a planewave impinging on a ring shaped aperture,which is placed on the focal plane of a lens(or,more generally,of a converging system).See:D.Mugnai and I.Mochi,Phys.Rev.E73,016606(2006).[11]F.Cardone and R.Mignani,Energy and Geometry,World Scientiﬁc Series in Contemporary Chemical Physics-Vol.22(2004).。

跑鞋矩阵图

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基于ABAQUS的水下爆炸计算仿真实例

Modeling Submerged Structures Loaded byUnderwater Explosions with ABAQUS/ExplicitDavid B. WoyakABAQUS Solutions Northeast, LLCAbstract: Finite element analysis can be used to predict the transient response of submergedstructures that are externally loaded by an acoustic pressure shock wave resulting from anUnderwater Explosion (UNDEX). This class of problem is characterized by a strong couplingbetween the structural motions and acoustic pressures at the fluid-structure wetted interface. The structural behavior is a combination of long time (low frequency) response dominated by anadded mass effect, short time (high frequency) response dominated by radiation damping, and intermediate time-frequency response where both added mass and radiation damping behaviorare present. For the finite element method to be useful, the analyst must develop modelingtechniques and procedures that yield accurate and computationally tractable solutions. Modeling procedures and guidelines were developed for use with an explicit dynamics code that offersadvanced features such as: pressure formulated acoustic elements, surface based fluid-structure coupling, surface based absorbing (radiation) boundaries, and automated incident wave loadingfor the fluid-structure wetted interface. The modeling guidelines address issues such as: locationof the fluid acoustic domain outer boundary, meshing of the acoustic domain, representation ofthe shock wave, and solution efficiency. These modeling procedures and guidelines aredemonstrated with an ABAQUS/Explicit analysis of an UNDEX experiment in which a submergedtest cylinder was exposed to a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993).General BackgroundABAQUS/Explicit is an efficient tool for simulating the transient response of structural-acoustic systems, of which the response of submerged structures loaded by acoustic shock waves resultingfrom an Underwater Explosion (UNDEX) is an important problem class. This paper provides abrief discussion on the general nature of the structural-acoustic interaction and describes modeling studies that address general Finite Element Analysis (FEA) requirements for the accuratesimulation of UNDEX problems. The studies described in this report have general application to awide range of structural-acoustic problems, not just the analysis of submerged structures. Anexample analysis of a submerged cylinder is used to illustrate an UNDEX problem.UNDEX analyses can be generally characterized as transient simulations of acoustic scattering behavior. However, the objective of an UNDEX analysis is to evaluate the response of thesubmerged structure and not necessarily the acoustic response. The finite element model for the external acoustic domain must be adequate to represent the influence of the water on the structural response. The discussion herein will be restricted to those cases where the external fluid behavesas a linear acoustic fluid with no cavitation. Therefore, the model of the external acoustic domainneed only be tailored to provide an accurate loading on the structure and does not need toaccurately represent the acoustic waves that will travel away from the structure. It should be noted2002 ABAQUS Users’ Conference1that procedures for UNDEX analyses which include fluid cavitation will be available inABAQUS/Explicit with the release of Version 6.3 (Prasad & Cipolla, 2001).The total acoustic pressure in the external fluid that results from an underwater explosion consistsof the known incident shock wave (incoming) pressure and the unknown scattered wave(outgoing) pressure. The scattered wave pressure consists of two parts, a reflected part that is associated with the shock wave interacting with an ideal rigid, immovable structure and avibratory part that results from the motions of the structure at the interface with the fluid. When cavitation is not present, it is desirable to let the external acoustic domain represent only thescattered portion of the total acoustic pressure. The shock wave incident pressure load is applieddirectly to the structural mesh at the fluid-structure wetted interface. Acoustic loads associatedwith the reflected part of the scattered pressure are applied to the fluid mesh at the wettedinterface. The full scattered pressure (reflected and vibratory) is obtained as the solution for theacoustic element pressure degrees of freedom, and the complete scattered pressure loading on the structure is generated through the fluid-structure coupling equations. The acoustic loads are a characteristic of the incident shock wave, and are obtained from the fluid particle accelerations ina direction normal to the surface that defines the fluid-structure wetted interface.In the discussion that follows the capability of ABAQUS/Explicit to efficiently perform UNDEX analyses is demonstrated. The ABAQUS features utilized in solving this class of problem are:1. Computationally efficient pressure based acoustic elements.2. Surface based automated acoustic-structure coupling.3. Acoustic-structure coupling for mis-matched meshes.4. Surface based impedance models for representing non-reflecting fluid boundaries.5. Automated shock wave loading at the fluid-structure interface.Acoustic Domain Outer BoundaryUNDEX problems are characterized by a strong coupling between the structural motions and acoustic pressures at the wetted interface. The system response in a strongly coupled structural-acoustic system can be described as being a combination of the following types of response:1. Late Time - Low Frequency: Characterized by structural wavelengths that aresignificantly shorter than the associated acoustic wavelengths. The effect of the externalfluid on the structure is that of adding an effective mass to the structure on the wettedinterface. The scattered energy within the acoustic domain remains near the structurewith very little energy radiating away from the structure.2. Early Time - High Frequency: Characterized by structural wavelengths that aresignificantly longer than the associated acoustic wavelengths. The effect of the externalfluid on the structure is to act as a simple radiation damper at the wetted interface. Mostof the scattered energy within the acoustic domain radiates away from the structure.3. Intermediate Time - Frequency: Characterized by structural wavelengths that are ofsimilar length compared to the associated acoustic wavelengths. The effect of the2002 ABAQUS Users’ Conference 2external fluid on the structure is that of adding both effective mass and damping to thestructure. Comparable levels of scattered energy remain near the structure and areradiated away from the structure.Due to the high density and bulk modulus of water the finite element model for an UNDEXanalysis must be capable of accurately simulating all three ranges of structural-acoustic response.It should be noted that for some other types of structural-acoustic analyses, where the fluid is verylight compared to the structure, not all response types may be of equal importance. For example,the added mass effect of air acting upon heavy structures is often of no consequence.The acoustic model for the outer boundary of the external fluid domain must provide adequatenon-reflecting behavior over all three time-frequency ranges. Non-reflecting outer boundarymodels are implemented in ABAQUS/Explicit (Version 6.2) via a surface based boundary impedance. ABAQUS has several imbedded surface impedance models, of which the circular and sphere types were used for analyses described herein. These impedance models are based upon the classical solutions for a 3-dimensional point source (sphere) and a 2-dimensional point source or3-dimensioanl linear source (circular). The default impedance model corresponds to a simpleplane wave radiation condition, which is well suit to simple acoustic tube test simulations.For the late time - low frequency response range, the extent of fluid contributing to the added massis largest for the longest structural response wavelength. Also, for the early time - high frequency response range, the longest structural response wavelength has the potential to generate efficient radiating acoustic waves with the longest wavelengths. Therefore, the location of the fluid meshouter boundary can be based upon the structure’s longest characteristic response wavelength. Ageneral guideline for locating the acoustic mesh outer boundary was developed by performing aseries of analyses representing the harmonic translational motion of a rigid infinite cylinder in aninfinite fluid domain. This type of motion is closely related to the transverse motion of a cylindersection for beam bending response modes. A 2-dimensional rigid cylinder cross section (10”radius) was placed within a circular fluid domain, for which the outer boundary was located at 2,3, and 4 cylinder radii. The fluid was water with a bulk modulus of 345,600 psi and a sound speedof 60,000 inches per second. ABAQUS/Explicit was used to drive the cylinder with a harmonicmotion until steady state conditions were achieved. Baseline analyses with very refined acousticmeshes were used to represent the exact solutions. The baseline analyses utilized linear acoustictriangle elements with approximately 42 element divisions per acoustic wavelength. The outer boundary for the baseline analyses was located two full acoustic wavelengths away from thestructure, and utilized the circular type impedance boundary. The boundary evaluation modelshad a minimum of 20 element divisions per acoustic wavelength for the highest driving frequency,and the maximum acoustic element size was set at 1.5 inches for the lowest driving frequencies.Figure 1 shows the baseline results for the complex radiation impedance of the driven cylinder(force/velocity). The impedance values are plotted against the ratio of the structural wavelength,which is the cylinder circumference, to the driving frequency acoustic wavelength. The radiation reactance (imaginary) represents an added-mass effect and the radiation resistance (real)represents the acoustic damping. Figure 1 clearly shows all three time-frequency response ranges,with the radiation impedance transitioning from added mass at low frequencies to radiationdamping at high frequencies. Figure 2 shows a plot of the error ratio for the radiation impedance predictions with the evaluation models. The radial thickness of the fluid mesh for the outerboundary at 2, 3 and 4 cylinder radii, corresponds to approximately 1/6, 1/3, and 1/2 of thestructural wavelength. Setting the boundary at 2 cylinder radii (1/6 structural wavelength) works2002 ABAQUS Users’ Conference3well at high frequencies but can introduce significant error in the added mass at low frequencies.The error oscillations within the 5% error range at the higher driving frequencies appear to be dueto the outer boundary being placed near integer multiples of half the acoustic wavelength. Placingthe outer boundary so that the fluid domain thickness is between 1/3 and 1/2 the largest structural wavelength provides for reasonable accuracy when using a sound source based outer boundarysurface impedance model. The performance when using a classical plane wave boundary conditionis significantly diminished, and would require at least doubling the extent of the fluid domain.Fluid Mesh Requirements for Representing the Shock WaveThe classical representation of a spherical shock wave associated with UNDEX loading is characterized by an instantaneous pressure rise to a peak value followed by an exponential decay.An UNDEX analysis in which the external fluid is modeled with finite elements cannot accurately represent a shock wave having an instantaneous pressure rise because the infinite pressure gradientat the shock front implies infinite fluid particle acceleration, so that the acoustic loads associatedwith the reflected part of the scattered pressure become indeterminate. Therefore, the shock frontmust be modeled such that the pressure rise occurs over a period of time, designated the “risetime”. A reasonable value for the rise time can usually be obtained from experimental oranecdotal data. The pressure vs. time history of the shock wave at a known distance form thesource can be used to evaluate element size requirements for the acoustic mesh. This isaccomplished by means of a simple acoustic tube evaluation model.A simple acoustic tube model was constructed with the linear tetrahedron acoustic elements thatwill be used in the subsequent UNDEX example analyses. Acoustic loads representative of aplanar shock wave are applied at one end of the model with the ABAQUS incident wave loading capability. The end at which the loads are applied represents a rigid immovable wall. Theresulting reflected wave travels down the acoustic tube. A simple plane wave absorbing boundarycan be applied to the opposite end of the tube, or the tube can be made of sufficient length so thatthe test analysis finishes before the reflected wave reaches the opposite end.Figure 3 shows the results for a tube analysis in which the nominal element size is equal to 1.5times the wave propagation distance corresponding to the rise time of the shock front. The onlyoutput quantity of concern in these acoustic tube analyses is the pressure at the rigid wall(scattered pressure). An ideal solution for this problem would have the reflected wave being anexact copy of the shock wave. This is clearly not the case for the Figure 3 model. Figure 4 isanother analysis with the element size set at 1/4 the rise time propagation distance. The scattered pressure matches the shock pulse very well. However, there is still a fair degree of oscillation inthe early time solution. It should be noted that the range in the pressure oscillations can become noticeably less when using brick type acoustic elements.Figure 5 shows some additional solutions with the element size set at 1.5 times the rise timedistance, for which the time increment was varied via direct user control. As the time increment is reduced the mean response approaches that of the incident shock wave. This illustrates howsimple acoustic tube models can also be used to evaluate the time increment requirements foraccurately representing the reflected wave loading. Figure 5 also suggests that a relatively coarsefluid mesh may provide sufficient solution accuracy for the structural response as long as thestructure being analyzed responds at low frequencies relative to the reflected wave oscillations.For these cases, the pressure impulse (time integral of pressure) associated with the reflected and2002 ABAQUS Users’ Conference 4incident shock waves should have relatively good correlation. Figure 6 shows the pressure impulse curves generated from the Figure 5 analyses, and suggests that using a time increment that is lessthan or equal to 1/20 of the rise time may provide good results with the coarse acoustic mesh for alow frequency structural system.Example Problem DescriptionThe UNDEX example problem is based upon an experiment in which a submerged test cylinderwas exposed to a shock wave produced by a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993). The test cylinder is made of T6061-T6 aluminum, has an overall length of 1.067 meters, an outside diameter of 0.305 meters, a wall thickness of 6.35 millimeters and welded endcaps that are24.5 millimeters thick. The cylinder was suspended horizontally in a 40-meter deep fresh watertest quarry (sound speed =1463 meters/second). The 60-pound HBX-1 explosive charge and the cylinder were both placed at a depth of 3.66 meters, with the charge centered off the side of thecylinder and located 7.62 meters from the cylinder surface. The suspension depths, charge offsetand duration of the test were selected such that cavitation of the fluid would not be significant andno bubble pulse would occur. During the UNDEX test, two pressure transducers were positioned7.62 meters from the charge, away from the cylinder, but at the same depth as the cylinder. These transducers provided an experimental determination for the pressure vs. time history of theincident spherical shock wave as it traveled by the point on the cylinder closest to the charge.Figure 7 is a time history of the recorded shock wave pressure used as input to theABAQUS/Explicit analyses. Strain gages were placed at several locations on the outer surface ofthe test cylinder, as shown in Figure 8. The strain gage experimental data was filtered at 2000 Hz,with the experimental data presented herein obtained by digitizing the published Kwon & Foxstrain data.ABAQUS/Explicit Model & ResultsThe test cylinder was meshed with 2400 S4R finite strain shell elements and contained 2402 nodes (14412 dof) on 40 circumferential and 53 axial element divisions. The element connectivity issuch that each shell normal is directed into the external fluid. The shell element nodes arepositioned on the outside surface of the test cylinder. The cylinder body elements directlyadjacent to the endcaps have reduced mass & stiffness and are only used to provide a surface that corresponds to the thickness of the endcaps. BEAM type MPCs are used to rigidly tie theendcaps to the main cylinder body.The external fluid is meshed with 4-noded AC3D4 acoustic tetrahedral elements. The outerboundary of the external fluid is represented by cylindrical and spherical surfaces with theappropriate surface impedance absorbing conditions. The characteristic radius of the fluid outer boundary is set at 3 shell radii, thus the thickness of fluid modeled about the cylinder represents approximately 1/3 of the cylinder’s outer circumference (rigid body translational wavelength).Based upon the mesh boundary study this location should be sufficient to provide reasonablyaccurate results. Figure 9 shows the cylinder and first acoustic mesh that was used in the analysis,with the top half of fluid removed for clarity. The shock wave rise time is 0.0182 milliseconds, corresponding to a wave propagation distance of 0.0266 meters. The nominal element size at thewetted interface is also set at 0.0266 meters and increases in size to a nominal 0.080 meters at the2002 ABAQUS Users’ Conference5outer fluid boundary. An acoustic element size of 0.080 meters corresponds to approximately 12 element divisions per acoustic wavelength for a 1500 Hz response. Figure 10 provides the resultsof the acoustic tube validation for this degree of mesh refinement. Acoustic Mesh #1 contains39186 elements and 7947 pressure degrees of freedom. Figure 11 shows the second acousticmesh that was used in the analysis, with the top half of fluid removed for clarity. The nominalelement size at the wetted interface is set at 0.010 meters and increases in size to a nominal 0.030meters at the outer fluid boundary. Figure 12 provides the results of the acoustic tube validation corresponding to acoustic Mesh #2, which contains 463114 elements and 87745 pressure degreesof freedom.Figure 13 shows the ABAQUS predicted axial strain response at strain gage location B1 whenusing the coarse (#1) and refined (#2) acoustic meshes. The response curves are very close both in magnitude and phasing. The close correlation between the two analyses was also apparent at theother strain gage locations. This indicates that for the applied UNDEX loading the structuralresponse times are long when compared to the reflected wave oscillations obtained in the acoustictube validation analyses. This result was predictable when considering an eigenvalue analysis forthe cylinder with no external fluid. The modes that have the greatest potential for producingdamage have frequencies well below 1500 Hz, and will be further reduced when the cylinder is submerged due to the added mass effect. The cylinder modes have response periods that are significantly longer than the shock wave rise time or reflected wave pressure oscillations. Thus,for this particular example, using an acoustic mesh and solution time increment that reasonablycaptures the shock wave reflected pulse and can represent the scattered acoustic waves at thestructural response frequencies is adequate for obtaining a good solution.The response shown in Figure 13 is dominated by the fundamental beam bending mode of thecylinder, for which the dominant motion is transverse to the cylinder axis. At any point along the cylinder axis the motion is dominated by a translation of the cross section through the fluid,similar to the motion used in the infinite cylinder modeling study. The only damping mechanismsin the analyses were due to acoustic radiation and the /Explicit default values for element bulk viscosity. The acoustic model does not include any losses due to hydrodynamic drag (fluidviscosity) associated with the motions of the cylinder. The effect of hydrodynamic drag on thelate time response of the cylinder is clearly shown in Figure 14, where the predicted axial strain response is compared to the experimental data. The experimental data was digitized from apublished curve (Kwon & Fox, 1993), and was shifted by 0.2 milliseconds in order to align the experimental and analysis time axes. The solution designated as ALPHA = 0, represents theoriginal analysis, whereas the analysis designated as ALPHA=750 utilized mass proportionaldamping (10% critical at 600 Hz) applied to the cylinder as an approximation for the effects of hydrodynamic drag. The application of ALPHA damping does not have an adverse effect on thesolution critical time increment. ALPHA damping does not significantly affect the early timeresponse (high frequency), but does significantly reduce the late time response (low frequency).This is consistent with what is observed with the experimental data. In any event, ignoring hydrodynamic drag in an UNDEX analysis will produce conservative (high) levels for thestructural response, which is often a desirable trait when doing a design evaluation analysis.Figure 15 shows the levels of Accumulated Plastic Strain (PEEQ) on the outer surface of the shellat the end of the analysis with fluid Mesh #1 and ALPHA= 750. No change occurs in the peakplastic strain level of the cylinder wall after the first 0.34 milliseconds. Recalling that the entireshock pulse duration is 2.0 milliseconds, this truly is an early time response. No change occurs inthe peak accumulated plastic strain of the endcaps after 2.84 milliseconds, which indicates that the2002 ABAQUS Users’ Conference 6endcap response may be influenced to a greater extent by the late time response. Unfortunately,there were no strain gages attached to the endcaps and the cylinder wall gages located in theregions of high plastic strain failed during the test. Table 1 compares the peak accumulated plasticstrains obtained with the two acoustic meshes, with and without ALPHA damping. The results comparison between Mesh #1 and Mesh #2 is very good. The effect of ALPHA damping on thecylinder wall PEEQ is very small, but is significant for the endcap response. Table 1 also providesa comparison of the solution times for the analyses, and illustrates the solution efficiency of theacoustic elements as compares to structural elements.ConclusionsABAQUS/Explicit provides an efficient means to evaluate the transient response of structural-acoustic systems loaded by external acoustic sources. This was illustrated with the analysis of a submerged cylinder acted upon by a shock wave generated by an underwater explosion. Themodeling studies presented in this paper indicate that sufficient accuracy for a submergedstructure’s response can be obtained when positioning the external absorbing boundary of theacoustic domain a distance from the structure of between 1/3 to 1/2 the longest characteristicstructural wavelength. Modeling studies also indicated that the degree of refinement in theacoustic domain mesh can be tailored to the characteristics of the shock pulse and the nature of structural response, i.e., short vs. long response times as compared to the shock pulse transient.Table 1. Model statistics and results comparisons.Item Cylinder Only Acoustic Mesh #1 Acoustic Mesh #2 No. Acoustic Elements N/A 39186 463114No. Acoustic DOF N/A 7947 87745No. Shell Elements 2400 2400 2400No. Shell DOF 14412 14412 14412Solution Time Increments 4730 4730 13873CPU Time (Seconds) 281 426 4590CPU per Increment 0.059 0.090 0.331PEEQ Cylinder Wall(Alpha = 750) N/A 0.00820 0.00810PEEQ Cylinder Wall(Alpha = 0) N/A 0.00838 0.00828PEEQ Endcap Center(Alpha = 750) N/A 0.00626 0.00611PEEQ Endcap Center(Alpha = 0) N/A 0.01007 0.009852002 ABAQUS Users’ Conference78 2002 ABAQUS Users’ ConferenceFigure 1. Baseline radiation impedance results for an infinite rigid cylinder.Figure 2. Error ratio for the radiation impedance evaluation models.2002 ABAQUS Users’ Conference 9Figure 3. Acoustic tube with elements 1-½ the rise time propagation distance.Figure 4. Acoustic tube with elements ¼ the rise time propagation distance.10 2002 ABAQUS Users’ ConferenceFigure 5. Additional results for 1-½ rise time element mesh.Figure 6. Pressure impulse curves from Figure 5 analyses.Figure 7. Incident shock wave pressure transient.Figure 8. Test Cylinder Strain Gage Locations.2002 ABAQUS Users’ Conference11Figure 9. Cylinder and acoustic Mesh #1.Figure 10. Acoustic tube validation results for Mesh #1. 12 2002 ABAQUS Users’ ConferenceFigure 11. Cylinder and acoustic Mesh #2.Figure 12. Acoustic tube validation results for Mesh #2. 2002 ABAQUS Users’ Conference 13Figure 13. Axial strain response at gage location B1.Figure 14. Comparison plots of response at strain gage B1.142002 ABAQUS Users’ ConferenceFigure 15. Accumulated plastic strain in the test cylinder.References1. Kwon, Y.W. and P.K. Fox, “Underwater Shock Response of a Cylinder Subjected to a SideOn Explosion,” Computers and Structures, Vol. 48, No. 4, 1993. 2. Prasad, B.R. Nimmagadda and J. Cipolla, “A Pressure Based Cavitation Model for Underwater Shock Problems,” Shock and Vibration Symposium, Paper U30, November, 2001.2002 ABAQUS Users’ Conference15。

SAEJ358-1991 非破坏性试验

SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8512 FAX: (724) 776-0243TO PLACE A DOCUMENT ORDER; (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS Copyright 1991 Society of Automotive Engineers, Inc.All rights reserved.Printed in U.S.A.SAE J358 Revised FEB91Increasing consumer demand for product quality at reasonable cost has resulted in development of nondestructive tests which can be applied to materials and manufactured parts. Although a variety of complementary nondestructive methods is available, development time is generally required for application to specific materials or products. The effect of part contour, surface condition, heat treatment, composition variation, and other variables may limit the ability of certain tests to detect imperfections with desired accuracy.Nondestructive tests properly applied to basic material can add greater assurance of performance to design strengths, thereby affecting material and manufacturing economy. In addition, parts can be tested after each basic operation which is critical to service performance of the finished part. In-process nondestructive tests can also serve as basic components of feedback process control systems since all tests are based upon measurements which do not damage the material or part being inspected.2.References2.1Applicable Publications—The following publications form a part of the specification to the extent specifiedherein. Unless otherwise indicated the lastest revision of SAE publications shall apply.2.1.1SAE P UBLICATIONS—Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001.SAE J369—Infrared TestingSAE J420—Magnetic Particle InspectionSAE J425—Electromagnetic Testing by Eddy Current MethodsSAE J426—Liquid Penetrant Test MethodsSAE J427—Penetrating Radiation InspectionSAE J428—Ultrasonic InspectionSAE J1242—Acoustic Emission Test MethodsSAE J1267—Leakage Testing-2-3.Notes3.1Marginal Indicia—The change bar (l) located in the left margin is for the convenience of the user in locatingareas where technical revisions have been made to the previous issue of the report. An (R) symbol to the left of the document title indicates a complete revision of the report.PREPARED BY THE SAE IRON & STEEL TECHNICAL COMMITTEE SUBCOMMITTEE 25 -NONDESTRUCTIVE TEST METHODS-5-Rationale—Not applicable.Relationship of SAE Standard to ISO Standard—Not applicable.Application—Nondestructive tests are those tests which detect factors related to the serviceability or quality ofa part or material without limiting its usefulness. Material defects such as surface cracks, laps, pits,internal inclusions, bursts, shrink, seam, hot tears, and composition analysis can be detected.Sometimes their dimensions and exact location can be determined. Such tests can usually be made rapidly. Processing results such as hardness, case depth, wall thickness, ductility, decarburization, cracks, apparent tensile strength, grain size, and lack of weld penetration or fusion may be detectable and measurable. Service results such as corrosion and fatigue cracking may be detected and measured by nondestructive test methods. In many cases, imperfections can be automatically detected so that parts or materials can be classified.The SAE Handbook describes the following nondestructive test methods:SAE J359—InfraredSAE J420—Magnetic ParticleSAE J425—Eddy CurrentSAE J426—Liquid PenetrantSAE J427—Penetrating RadiationSAE J428—UltrasonicSAW J1242—Acoustic EmissionSAE J1267—Leakage TestingTable 1 summarizes the principal features of most of these tests. In addition to the tests described, other nondestructive tests exist which are less well established, but whose use is expanding. Among these are microwave tests, holography, and sonic tests. Microwaves are used to locate defects in nonmetallic substances and to determine some physical characteristics of those materials. Optical holography uses coherent light from a laser beam to detect strains and defects in materials by means of three-dimensional imaging and interferometry techniques. Acoustical holography uses ultrasonic waves to image discontinuities in the interior of solids. Recent refinements in sonic testing permit more objective determination of the physical properties of cast iron. Complete information concerning each nondestructive test can be obtained from books listed in the bibliographies of the aforementioned reports.Increasing consumer demand for product quality at reasonable cost has resulted in development of nondestructive tests which can be applied to materials and manufactured parts. Although a variety of complementary nondestructive methods is available, development time is generally required for application to specific materials or products. The effect of part contour, surface condition, heat treatment, composition variation, and other variables may limit the ability of certain tests to detect imperfections with desired accuracy.Nondestructive tests properly applied to basic material can add greater assurance of performance to design strengths, thereby affecting material and manufacturing economy. In addition, parts can be tested after each basic operation which is critical to service performance of the finished part. In-process nondestructive tests can also serve as basic components of feedback process control systems since all tests are based upon measurements which do not damage the material or part being inspected.Reference SectionSAE J359—Infrared TestingSAE J420—Magnetic Particle InspectionSAE J425—Electromagnetic Testing by Eddy Current MethodsSAE J426—Liquid Penetrant Test MethodsSAE J427—Penetrating Radiation InspectionSAE J428—Ultrasonic InspectionSAE J1242—Acoustic Emission Test MethodsSAE J1267—Leakage TestingDeveloped by the SAE Iron & Steel Technical Committee Subcommittee 25—Nondestructive TestMethodsSponsored by the SAE Iron & Steel Technical Committee。

群论英文

LIE GROUPS IN PHYSICS1
version 25/06/07
Institute for Theoretical Physics Utrecht University Beta Faculty
2007
English version by G. ’t Hooft Original text by M.J.G. Veltman B.Q.P.J. de Wit and G. ’t Hooft
pions mπ+ ≈ 140 MeV/c2 mπ0 ≈ 135 MeV/c2 mπ− ≈ 140 MeV/c2
∆ particles m∆++ ≈ 1231 MeV/c2 m∆+ ≈ 1232 MeV/c2 m∆0 ≈ 1233 MeV/c2 m∆− ≈ 1235 MeV/c2
Table 1: Masses of nucleons, pions and ∆ particles, expressed in MeV/c2 . two possible decay modes: ∆+ → n π + and ∆+ → p π on 2 Quantum mechanics and rotation invariance 3 The group of rotations in three dimensions 4 More about representations 5 Ladder operators 6 The group SU (2) 7 Spin and angular distributions 8 Isospin 9 The Hydrogen Atom 10 The group SU(3) 11 Representations of SU(N); Young tableaus 12 Beyond these notes 1 7 14 22 26 31 39 45 48 55 60 61

圆盘法测量介电常数

3126IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009Broadband Characterization of Complex Permittivity for Low-Loss Dielectrics: Circular PC Board Disk ApproachZhonghai Guo, Guangwen (George) Pan, Stephen Hall, and Christopher PanAbstract—We present a nondestructive method for determination of the permittivity and loss tangent of low-loss dielectrics using printed circuit board (PCB) circular disks. Because it utilizes multiple resonances, this method is in high precision and broadband (500 MHz–12 GHz), covering the UHF, GSM 850/1800, 802.11b/g, WiMax, WLAN, and UWB bands. The method is simple and accurate based on closed-form analytic expressions of cylindrical symmetry, taking into account disk rim fringing ﬁelds and radiation loss. Numerical results are conducted for popular PCB material, FR4, and the self-consistent Kramers–Kronig (KK) relation is veriﬁed. Index Terms—Dielectric measurements, high-speed digital circuit, loss tangent, microwave measurements, real permittivity, selfconsistency.I. INTRODUCTION HE complex permittivity of dielectrics plays important roles in the modeling, design, fabrication, and testing of antennas, microwave circuits, and high-speed digital systems, in particular for wireless communications. Accordingly, extensive research has been conducted in the past decades [1]–[10]. To date, the popular measurement techniques in the RF and microwave region are cavity resonator, transmission line, free space, and open-ended coaxial probe, among others. Each method has its unique pros and cons. For instance, the advantage of high Q resonant method is its high accuracy, but the measurement can only be performed at a single frequency for each laboratory setup. Recently, a broadband split cylinder resonant technique is reported, which is nondestructive. Nevertheless, the method is quite complicated in terms of apparatus and operations [2]. Transmission line technique, as a nondestructive approach, seems to be simple for broadband characterization. However, it lacks precision. The free-space technique may suffer from electromagnetic interference, while the open-end coaxial probe method may not be suitable for extremely low-loss materials [6].Manuscript received February 19, 2008; revised November 26, 2008. First published July 28, 2009; current version published October 07, 2009. This work was supported by Intel Physical Technologies Lab, Hillsboro, OR. Z. Guo and G. Pan are with the Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail: zguo2008@; george.pan@). S. Hall is with Intel Physical Technologies Lab, Hillsboro, OR 97124 USA. C. Pan is with Qualcomm, San Diego, CA 92121 USA Color versions of one or more of the ﬁgures in this paper are available online at . Digital Object Identiﬁer 10.1109/TAP.2009.2028525TA simple and practical method for determination of the dielectric constant and loss tangent was unfolded, utilizing thin dielectric ﬁlms embedded in a rectangular parallel-plate capacitor. This work was developed based on the measured admittance of a capacitor [8], [9]. However, this model is only valid when the operating frequencies of the rectangular parallel-plate structure are far below the ﬁrst resonant frequency. To overcome such a constraint, a high-order-mode analytical method was developed based on full-wave analysis [10], using closed-form analytical expressions for the impedance near each high-order modal resonant frequency, at which the impedance contribution from the resonant mode dominates. Despite its advances, this method treats the fringing ﬁeld via an equivalent electric width, which only accounts for the additional susceptance. This will make the loss tangent less accurate because the power loss due to radiation is neglected. In addition, rectangular parallel-plate-structure-produced S-parameter curves are in irregular patterns. The frequency interval between two neighbor peaks of the curve is quite irregular: Some peaks are closer to each other, while others are far apart; some lobes are larger, while some are much thinner. This makes the algorithm difﬁcult to extract the complex permittivity effectively. In this paper, we extended the investigation of [10] and replaced the rectangular geometry with circular. As a result, a high-ﬁdelity broadband nondestructive method has been developed for measuring the permittivity and loss tangent of dielectrics. The new method is simple, accurate, robust, and repeatable because we take the advantage of highly symmetrical conﬁguration and nearly closed-form analytical solutions. The method is applicable to a wide frequency range from 0.5 to 12 GHz, which covers the UHF, GSM 850/1800, 802.11b/g, WiMax, WLAN, and UWB bands for wireless local area networks. Although the investigated frequency range is 500 MHz–12 GHz, higher frequency is also possible, governed by (1) in the next section. Fig. 1 is the laboratory setup of this circular printed circuit board (PCB) disk approach.II. FORMULATION OF CIRCULAR PARALLEL-PLATE METAL-DIELECTRIC STRUCTURE The cross-section view of the circular copper-dielectric sandis the diameter of wich structure is shown in Fig. 2, where the top and bottom copper plates, is the thickness of dielectric layer marked with gray color, and and are respectively the diameter of the central conductor and interior wall diameter0018-926X/$26.00 © 2009 IEEEAuthorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.GUO et al.: BROADBAND CHARACTERIZATION OF COMPLEX PERMITTIVITY FOR LOW-LOSS DIELECTRICS3127Fig. 3. Admittance for disk h : mm, c : mm accounting for radiation. The positive susceptance means the equivalent load is capacitive. Fig. 1. Measurement conﬁguration with coaxial feed in the lab.= 1 524= 152 4where is the electrical vector potential, the superscript implies magnetic current as source, , is the angular frequency, and is the wavenumber in the substrate under test and is expressed in terms of real relative permittivity and loss as tangent (3)Fig. 2. Circular parallel-plate structure with a feeding coaxial line.of the coaxial cable. The structure is modeled as a symmetrically excited E-type radial waveguide terminated by an equivalent wall admittance appropriate for the radiating aperture along the open edge [11]. A comprehensive analysis of coaxial-fed radial-line terminated with arbitrary load is detailed in [12]. Exact computations of the terminating admittance due to the radiation on the aperture involve considerable mathematical difﬁculties. To derive the equivalent admittance of the radiation aperture and to obtain a complete solution of circular parallel-plate structure with coaxial feed, we have made two reasonable assumptions: 1) The ﬁelds outside the disk are mainly generated by the equivalent magnetic current related to the tangential electric ﬁeld on the rim aperture. 2) The only coupling between the source and load is due to the dominant mode, and the tangential electric ﬁeld distribution on the rim aperture is only by the dominant mode. Based on this assumption, the thickness of substrate should meet (1) is the highest frequency of interest, is freewhere space permeability, and is the complex permittivity to be determined. These assumptions are validated by numerical results of the in-house FEM codes in Section III. A. Equivalent Admittance of the Radiating Aperture Based on the assumptions above, we obtain the magnetic ﬁeld outside the disk due to the equivalent magnetic current on the apertures (2)is the dielectric permittivity in the vacuum. The where most important parameter in the derivation as well as in the whole paper is the complex-valued , but it is “hidden” in the wavenumber. We will try to determine it uniquely, effectively, and accurately. Because of symmetry in geometry and the assumption of only dominant mode on the aperture, we may get the magnetic ﬁeld on the radiation aperture as(4)where is the surface on the side wall of the disk (radiation aperture), and primed and unprimed variables are for source and ﬁeld point, respectively. The superscript represents dominant is the dominant mode ﬁeld at the disk edge mode, namely , , . in cylindrical coordinates is the equivalent magnetic current on the aperture. The Green’s function is given as (5) Using the continuity of tangential magnetic ﬁeld across the radiation aperture, we may write the load admittance appropriate for the radiation aperture as (6)Fig. 3 shows the calculated wall admittance versus frequency for the structure ﬁlled with popular PCB material, FR4 ( , ). The positive susceptance means that the load is capacitive.Authorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.3128IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009B. Input Admittance and Field Distributions In our theoretical model, we make the TEM approximation for the excitation, which is reasonably accurate [13], [14]. Under the TEM assumption, the normalized radial electrical ﬁeld (7) In the equation above and in the following derivation, the noris made. After lengthy and temalization dious derivations, we may write the ﬁeld distribution in the parallel plate in two regions in terms of Bessel’s functions as: (i) The regionwhere , and,,(14) (15) (16) (17)(18) where is the characteristic impedance of radial line at , is the equivalent impedance of the raare diation aperture, and , , , , , , , and Bessel’s and modiﬁed Bessel’s functions. The admittance seen from the coaxial line in the reference plane (see Fig. 2) is given by [15](8)(19) Substituting (10) into (19), we may write the input admittance as (20) where (21) is the susceptance of short-circuited coaxial line with length ; (22) is the admittance contribution of matched radial-line dominant mode;(9)(10) (ii) The region(11) is the susceptance contribution of cutoff radial-lines modes; (12) (23) is the admittance contribution of the radiation aperture at . edge C. Relative Permittivity (13) It is observed that the oscillation phenomena of input admittance or the S-parameter curve are introduced by the loadAuthorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.GUO et al.: BROADBAND CHARACTERIZATION OF COMPLEX PERMITTIVITY FOR LOW-LOSS DIELECTRICS3129, real power delivered to the DUT from the The input power coaxial aperture, is(29) Referring to (19), we get a relation between the power and normalized input conductance (30) which must be equal to the sum of conductor loss of , radiand dielectric loss of . The loss terms are ation loss of evaluated, using perturbation theoryjS j as a function of permittivity: tan b = 2:1 mm, c = 152:4 mm, h = 1:524 mm.Fig. 4.= 0:02,a= 0:35 mm,presenting the radiation aperture. At the peaks of the input con, the imaginary part of . Furtherductance curve more, the peaks are only determined by the real relative perpattern as a function for mittivity . Fig. 4 depicts the different operating frequencies. To enforce this condition, we and substitute it into (23), yielding write (24) where (25) (26) (27) (28) It should be emphasized that (24) is an implicit equation of frequency-dependent complex permittivity , which is related to the wavenumber, , via (3). There are two ways to use this condition. One is to search the frequency points of peaks/nulls, when dielectric permittivity is known. The other way is to search the permittivity of the dielectric material in the disk when fre, we quency points are known. Through the measurement of know the frequency positions related the peaks of input conductance, we can use this equation to solve the real relative permittivity with a reasonable guess value of loss tangent. Since one cannot analytically solve the real relative permittivity using (24), the iterative method is employed; in our case, the NewtonRaphson technique. D. Loss Tangent In the previous subsection, we have outlined the procedure to determine the material relative permittivity of the device under test (DUT) from the measured data. Here, we summarize how to determine the loss tangent of the DUT based on measured data and the modal admittance relations. As usual, the small perturbation is in use. In the derivation of ﬁeld distributions and eigenequation (24), we assume that the plates are perfect conductors. As loss tangent is concerned, we must face the ﬁnite conductivity of the metal plates. For highconductivity metals, the ﬁelds should only slightly differ from that of perfectly conducting metals, and we use the expressions above for the electric and magnetic ﬁelds without modiﬁcations.(31)(32)(33)(34) where superscripts represent dominant mode and 1 and 2 reis the spectively imply region 1 and 2 in subsection B, and admittance on the aperture accounting for radiation. Figs. 5 and 6 show the percentage of power loss versus frequency for each kind of dissipation mechanism under two different material loss tangent values of 0.01 and 0.001, respectively. These results reveal that while conductor loss is signiﬁ-Authorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.3130IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009Fig. 7. Conﬁguration of perfectly matched radial line.Fig. 5. Percentage of three types of dissipated power with the parameters: : , tan : , a : mm, b : mm, c : mm, h : mm.44 1 524= 0 01= 0 35= 21= 152 4= =Fig. 8. FEM conﬁguration of radiation of radial line with PML truncation.44 1 524Fig. 6. Percentage of three types of dissipated power with the parameters: : : , tan ,a : mm, b : mm, c : mm, h : mm.= 0 001= 0 35= 21= 152 4= =dominant mode approximation and perfectly matched load at the terminal, we take the circular disk as a nonuniform transmission line. Hence, the outward radial impedance at radius is equal to the ratio of outgoing voltage wave to outgoing curis deﬁned as rent wave. The load (35)cant in the low-frequency region, radiation loss becomes comparable to dielectric loss for extremely low-loss dielectrics. We wish to have high percentage of dielectric loss in order to maintain a high resolution of loss tangent determination. The increase of conducting and radiation loss will decrease the percentage of the dielectric loss, which in turn may increase the numerical error in extracting the loss tangent. However, the simulation results of Fig. 6 show that even for extremely low-loss ma, there is sufﬁcient percentage of terial with (18%–40%) to calculate the loss tangent quite accurately with this model. III. NUMERICAL SOLUTION OF CIRCULAR PARALLEL-PLATE STRUCTURE The simplicity of our algorithm is based on analytical expressions, which are the results of TEM radial line. In this section, we develop the FEM codes to validate the quasi-TEM model of the radial line, namely the TEM approximation of the excitation at the coaxial aperture and radiation along the disk rim wall. Here, we still make the assumption that the ﬁeld are uniform along the azimuth direction . At the same time, to take advantage of the axial symmetry, we formulate the FEM problem only in 2D, corresponding to its angular cross section with the aid of the Fourier expansion. Here, in the FEM model, we address the two problems of coaxial feed and radial line radiation. Fig. 7 shows the conﬁguration of the circular disk, where the at . Under the radial line is perfectly matched to a loadFor more detailed discussions, readers are referred to [16]. We make the port of coaxial line far enough from the junction to allow high-order modes to evanesce adequately. We then compare the input admittance resulting from analytic and numerical solutions to check the accuracy of the TEM model. Fig. 8 illustrates the FEM conﬁguration to study aperture radiation, where the perfectly matched layer (PML) in the cylindrical coordinate system has been implemented to truncate the open region. Thus, the effect of radiation can be computed accurately. Based on the solutions of the problem in Fig. 7, we know how accurate the TEM approximation is. Then, we compare the resulting input admittance of the FEM model with that of analytic approximation to estimate the precision of the load on the radiation aperture. A. Formulation of FEM In accordance with the variational principle [17], the functional for the electric ﬁeld is given by(36)Authorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.GUO et al.: BROADBAND CHARACTERIZATION OF COMPLEX PERMITTIVITY FOR LOW-LOSS DIELECTRICS3131where , is the surface of coaxial port, is the surface of side wall that is only used when we solve the problem . Here, the is the TEM in Fig. 7, and mode distribution on the surface of coaxial port . In (36), the PML is conveniently interpreted as an anisotropic medium [18], [19]. Using this interpretation, the constitutive parameters take the form [20] (37) with (38) and the parameters inside PML are given by (39) (40) (41) , , and where is the PML thickness; are the locations of the air-to-PML interfaces; and is a real parameter to be selected to optimum the efﬁciency of PML [19]. . Outside PML, we set In our computation, we choose , , and . Because of the axial symmetry, both the electric and magnetic ﬁelds can be represented by the Fourier series (42) (43) where subscript stands for transverse, namely ﬁelds in the plane that is transverse to the direction. Since ﬁrst we have made the assumption that all the ﬁelds are uniform along the azimuth direction, we only need to calculate the fundamental mode. The only nonzero ﬁeld components are and . We can simplify this functional asFig. 9. FEM mesh for problem of Fig. 7: a mm, h : mm.30= 1 524= 0:35 mm, b = 2:1 mm, c =60 mm, h = 1:524 mm.Fig. 10. FEM mesh for problem in Fig. 8: a= 0:35 mm, b = 2:1 mm, c =gular cross section into small triangular elements, the transverse Fourier component of the electric ﬁeld within each element can be expanded as (45) where the superscript denotes the element number, and denotes the edge basis function whose unknown . expansion coefﬁcient is Substituting (45) into (44) and then applying the variational principle, we obtain the matrix equation (46) The matrix blocks related to each element and segment are calculated as(47) (48) (49) where and are the cylindrical radius of local nodes on the segment, and and are the z coordinate values of local nodes on the segment. Figs. 9 and 10 show that triangular meshes have controlled size according to ﬁeld distributions; in the regions ﬁeld varying rapidly, meshes are ﬁner. The electrical ﬁeld distribution in Fig. 11 demonstrates that high-order modes due to discontimm since the nuity at the junction have died down at electric ﬁeld distribution is already the same as TEM mode in the coaxial line. Therefore, Fig. 8 provides accurate results(44) are respectively coaxial and disk rim apertures, . As a result, the volume integral in (36) is reduced to a surface integral over the angular cross section, and accordingly the surface integral is reduced to a line integral. After we divide the anwhereAuthorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.3132IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009Fig. 11. Electric ﬁeld distribution near junction when radial line impedance is : , : ,f GHz. perfectly matched: = 4 4 tan = 0 02 = 9Fig. 14. Input susceptance when radial line is perfectly matched: : .tan = 0 02= 4:4,Fig. 12. Electric ﬁeld distribution around the disk rim when radial line is open : , : ,f GHz. ended. = 4 4 tan = 0 02 = 9Fig. 15. Input conductance when radial line is open ended: : .0 02= 4:4, tan =Fig. 13. Input conductance when radial line is perfectly matched: : .tan = 0 0216. = 4:4, Fig. 0:02.Input susceptance when radial line is open ended: = 4:4, tan =of the reﬂection coefﬁcient using TEM excitation at the port mm. Fig. 12 illustrates that the dominant position mode approximation on the aperture is reasonably accurate in computing the external radiated magnetic ﬁeld to get the equivalent wall admittance. In fact, the ﬁeld distribution around the disk rim does not change sharply crossing the aperture from interior to exterior of the disk, and the electrical ﬁeld distribution on the aperture is very close to that of the dominant mode of the radial line. B. Numerical Results In Figs. 13–16, we compare the analytical results based on the TEM approximation and numerical results from the FEM , codes, in terms of input conductance and susceptance at for both matched impedance and open-ended cases in a largefrequency span. It can be seen clearly that the theoretical model is very accurate. IV. PERMITTIVITY AND LOSS TANGENT OF FR4 Using the algorithm developed in the previous sections, we determined the complex permittivity of the popular PCB material, FR4, from a copper-FR4-copper sandwich disk of 152.4 mm diameter and 1.524 mm substrate thickness. Although the investigated frequency range is 500 MHz–12 GHz, higher frequency range is also applicable. Figs. 17 and 18 respectively show magnitude and phase of measured from a vector network the scattering parameter analyzer HP8510C. Using the measured S-parameter data, we convert them into the input admittance seen from the coaxial port, which is demonstrated in Fig. 19. The extracted relativeAuthorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.GUO et al.: BROADBAND CHARACTERIZATION OF COMPLEX PERMITTIVITY FOR LOW-LOSS DIELECTRICS3133Fig. 17. Measured data of jS h : mm.= 1 524j:a= 0:35 mm, b = 2:1 mm, c = 152:4 mm,Fig. 20. Final results of relative permittivity of FR4.Fig. 18. Measured phase of S : a h : mm.= 1 524= 0:35 mm, b = 2:1 mm, c = 152:4 mm,Fig. 21. Final results of loss tangent of FR4.. (i) is analytic in the lower half-plane. (ii) The function when is real and . (iii) . (iv) Due to causal nature of the response of materials to electromagnetic ﬁelds, the real and imaginary parts of the complex dielectric permittivity couple each other through the KK relation as (50)Fig. 19. Input admittance seen from the coaxial port based on measured S : a : mm, b : mm, c : mm, h : mm.= 0 35=21= 152 4= 1 524(51) where stands for the principle value. For convenience, the . Then, a function is mapping from to is made: introduced aspermittivity is shown in Fig. 20. Then, we obtain the loss tangent of FR4 shown in Fig. 21, from 500 MHz to 12 GHz. V. SELF-CONSISTENCY CONFIRMATION Finally, we check the self-consistency of complex permittivity extracted from our method. Here, we introduce the ﬁnite frequency range Kramers–Kronig (KK) relations, namely bounds on the dispersion [21]. Unlike the classic KK dispersion relations, we only need the measurement data over a ﬁnite frequency range. This method can provide highly accurate interpolation formulas for the real part, given its value at a few selected frequencies and given the imaginary part over a range of frequencies. The only disadvantage is that we can only calculate the real part through the imaginary part, not vice versa. As we know, the complex dielectric permittivity has the following well-known properties:(52) The dispersion relation for given is (53) Now, suppose we already know in an interval of frequencies , then a computable estimate for is (54)Authorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.3134IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009The difference between functionandis deﬁned as discrepancy(55)The discrepancy function has the following properties: . (i) is an analytic function in the whole complex plane, (ii) on the real axis. except the set (iii) . The third item is based on the property of complex permittivity . at inﬁnite frequency, which is . Now, we try to use rational functions to approximate In order to get highly accurate interpolation by using only a in the ﬁnite frequency interval, we few selected points of choose those rational functions whose properties are the same . The rational functions to be employed should as that of meet the following conditions: (i) Have an equal number of poles and zeros that are all simple and located along the nonnegative real axis. (ii) The poles and zeros interlaced with a pole near (or at) the origin and a zero near (or at) inﬁnity. . (iii) No poles lie in the interval (iv) Each pole has a negative real residue. , . According to Suppose we already know the requirements above, we build the rational function approxias mation (56)Fig. 22. Upper and lower bounds obtained from four-point interpolation, showing self-consistency.simple with analytical expressions. The TEM assumption has been validated by the FEM model of the full-wave solution of circular parallel-plate structure. A copper-FR4-copper sandwich disk is used as the device under test for laboratory measurement utilizing the HP-8510C network analyzer, and the resulting data of frequency dependent permittivity and loss tangent are veriﬁed to satisfy the self-consistency property. ACKNOWLEDGMENT The authors wish to thank Intel Physical Technologies Lab, Hillsboro, OR, for material and technical support during the course of investigation. REFERENCES[1] W. Xi, W. R. Tinga, W. A. G. Voss, and B. Q. Tian, “New results for coaxial re-entrant cavity with partially dielectric ﬁlled gap,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 4, pp. 747–753, Apr. 1992. [2] M. D. Janezic, E. F. Kuester, and J. Baker-Jarvis, “Broadband complex permittivity measurements of dielectric substrates using a splitcylinder resonator,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, Jun. 2004, pp. 1817–1820. [3] K. M. C. Branch, J. Morsey, and A. C. Cangellaris, “Physically consistent transmission line models for high-speed interconnects in Lossy dielectrics,” IEEE Trans. Adv. Packag., vol. 25, no. 2, pp. 129–135, Aug. 1990. ´ and R. M. Biljic ´ , “Wideband frequency-domain char[4] A. R. Djordjevic acterization of FR-4 and time-domain causality,” IEEE Trans. Electromagn. Compat., vol. 43, no. 4, pp. 662–667, Nov. 2001. [5] J. Baker-Jarvis and E. J. Vanzura, “Improved technique for determining complex permittivity with the transmission/reﬂection method,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 8, pp. 1096–1103, Aug. 1990. [6] K. Staebell, M. Noffke, and D. Misra, “On the in situ probe method for measuring the permittivity of materials at microwave frequencies,” in Proc. IEEE. Instr. Meas. Technol. Conf., 1990, pp. 28–31. [7] S. B. Kumar, U. Raveendranath, P. Mohanan, and K. T. Mathew, “A simple free-space method for measuring the complex permittivity of single and compound dielectric materials,” Microw. Opt. Technol. Lett., vol. 26, no. 2, pp. 117–119, Jul. 2000. [8] P. K. Singh et al., “High frequency measurement of dielectric thin ﬁlms,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., San Diego, CA, May 1994, pp. 1457–1460. [9] W. Williamson, III et al., “High frequency dielectric properties of thin ﬁlm PZT capacitors,” Integrated Ferroelectronics, vol. 10, pp. 335–342, 1995. [10] R. Voelker, G. Lei, G. Pan, and B. Gilbert, “Determination of complex permittivity of low-loss dielectrics,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 10, pp. 1995–1960, Oct. 1997. [11] T. Fujimoto and K. Tanaka, “Wall admittance of a circular microstrip antenna,” Trans. Commun., vol. E82-B, no. 5, pp. 760–767, May 1999. [12] A. G. Williamson, “Radial-line/coaxial-line junctions: Analysis and equivalent circuits,” Int. J. Electron., vol. 58, no. 1, pp. 91–104, 1985.is the prescribed poles. , , or . Using (56), we get a matrix equais obtained. Corretion from which the approximation of sponding to the way to choose prescribed poles, there are eight . We discard those possibilities for a given value of values resulted from , which cannot meet the above requirement. The minimum value of what’s left forms the lower bound of this approximation, and the maximum value of what’s left forms the upper bound of this approximation. Then, after we translate these bounds back to the original variables, we get the sharpest possible bounds of real permittivity. Fig. 22 shows the lower and upper bounds of the real part of calculated by using the imaginary complex permittivity part of complex permittivity . This curve shows that the complex permittivity obeys the self-consistency quite well. where VI. CONCLUSION In this work, we developed a new algorithm of high-ﬁdelity characterization of low-loss dielectrics suitable for ultra-broadband covering the UHF, WWAN/WCDMA, WiMax, WLAN, and UWB bands. We use the circular PC board approach, based on the quasi-TEM radial line, which is accurate, practical, andAuthorized licensed use limited to: Arizona State University. Downloaded on October 9, 2009 at 19:57 from IEEE Xplore. Restrictions apply.。

非线性Schrodinger-MKdV方程的Hamilton结构及代数几何解

非线性Schrodinger-MKdV方程的Hamilton结构及代数几何解岳超【摘要】由3×3等谱Lax矩阵导出了非线性Schr?dinger-MKdV(NLS-MKdV)方程族,应用迹恒等式得到了其Hamilton结构.为方便构造代数几何解,我们将3×3矩阵等谱问题转化为等价的2×2问题,借助Riemann theta函数,求出了耦合的NLS方程及耦合的MKdV方程的代数几何解.【期刊名称】《聊城大学学报（自然科学版）》【年(卷),期】2019(032)001【总页数】8页(P30-37)【关键词】迹恒等式;Hamilton结构;代数几何解;Riemanntheta函数【作者】岳超【作者单位】泰山医学院医学信息工程学院,山东泰安271016【正文语种】中文【中图分类】O175.20 IntroductionSearching for the exact solutions of nonlinear equations has been important and interesting in the areas of the mathematics and physics，and several systematic methods have been developed to obtain explicit solutions of soliton equations， for instance， the inverse scattering method[1]，Darboux and Bäcklund transformations[2]，Hirota’s bilinear method[2-4]， Lie symmetry analysis etc [5-12]. The algebraic-geometric method was first developed by Matveev et al.as an analog of the inverse scattering theory.As a degenerated case of the algebro-geometric solutions， the multi-soliton solution and periodic solution in elliptic function type may be worked out.A systematic approach， proposed by Gesztesy and Holden to construct algebro-geometric solutions for integrable equations， has been extended to the whole (1+1) dimensional integrable hierarchy， such as the AKNS hierarchy， the Camassa-Holm hierarchy etc[13].Recently， Fan etc.investigated algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy， the Hunter-Saxton hierarchy and so on[14-17].In this paper，we first use a 3×3 isospectral Lax matrix to obtain a NLS-MKdV hierarchy by use of the Tu scheme[18-23]， which can reduce to the coupled NLS equation and coupled MKdV equation and whose Hamiltonian structure can be generated by applying the trace identity.As we know， constructing algebro-geometric solutions associated with the 3×3 matrix isosp ectral problem is more complicated than that related to the 2×2 case，hence we transform the above 3×3 matrix isospectral problem into an equivalent 2×2 one， by using Riemann theta functions，the algebro-geometric solutions of the coupled NLS equation and coupled MKdV equation are obtained easily.1 The NLS-MKdV hierarchy and its Hamiltonian structureConsider the 3×3 isospectral Lax matrix(1)solving the equation Vx=[U，V]，leads to(2)(3)Notea direct calculation may show that the compatibility conditions of the Lax pairs engenders the integrable hierarchy，(4)where J is a Hamiltonian operator， from (3)， we obtain a recurrence operatorTherefore， expression (4) can be written as(5)Reduction case 1 When n=2， the system (5) reduces to the following coupled NLS equation(6)Taking we obtain the NLS equationiRt2+2Rxx+R=0.Reduction case 2 When taking n=3 in (5)， we have the coupled MKdV equation(7)Taking β=1，q=0， we get the MKdV equation rt3-3r2rx-2rxxx=0.Hence we call the system (5) NLS-MKdV hierarchy.A direct computation yields=2b+2c，substituting the above equations into the trace identity [18]， we get(8)Comparing the coefficients of λ-n-1 on both sides in (8) leads toit is easy to find that γ=0， then we haveHence， we obtain the Hamiltonian structure of (5)(9)It is easy to verify that JL=L*J， so the NLS-MKdV hierarchy is integrable in Liouville sense.In the following section， we are interested in constructing algebro-geometric solutions of the coupled NLS equation (6) and the coupled MKdV equation (7).2 Algebro-geometric solutions of the coupled NLS equation (6) and the coupled MKdV equation (7)For calculation convenience，we transform 3×3 matrix isospectral problem (1) into an equivalent 2×2 one，(10)which can also generate equations (6) and (7).We consider the Lenard gradient sequence by the recursion relationKSj-1=JSj，Sj|(q，r)=0，S0=(2β，0，0)T ，(11)whereIt is easy to find that Sj is uniquely determined by the recursion relation (10).Here the condition Sj |(q，r)=0 is used to select the integration constant to be zero.A direct computation shows from (11) thatWe suppose (10) has two basic solutions X=(X1，X2)Tand Y=(Y1，Y2)T，thensatisfies the Lax equationWx=[U，W]， Wtm=[V(m)，W]，(12)which implies that the function det(W) is a constant independent of x andtm.From (12)， we get2gx=(q+r)h+(r-q)f，fx=λf-(q+r)g，hx=-λh+(q-r)g，(13)andgtm=B(m)h-C(m)f， ftm=2A(m)f-2B(m)g， htm=2C(m)g-2A(m)h，(14)where(15)and N is an arbitrary positive integer value.Substituting (15) into (13) gives KQj-1=JQj， JQ0=0 ， KQN=0， Qj=(aj，bj，cj)T.(16)It is clear to find JQ0=0 that has the general solutionQ0=α0S0=α0(2β，0，0)T，(17)from (11) and (16)， we have(18)where a0，…，ak+1 are integral constants.Substituting Eq.(18) into Eq.(16) yields the following certain stationary evolution equation(19)without loss of generality we set a0=1， from Eqs.(15)， (16)and (18)， we then have(20)By applying (15) we can rewrite f and h as the following finite products(21)By comparing the coefficients of λN-1，λN-2 and combining Eqs.(15) and (21)， we get(22)(23)since det (W) is a (2N + 2) th-order polynomial in λ with constants， we have(24)Substituting Eq.(15) into Eq.(24) and comparing the coefficient of λ2N+2，λ2N,gives(25)hence we obtain(26)From (24)we have(27)Again utilizing (13) and (21)， we find(28)which together with (27) leads to(29)Similarly， by use of (14)， (21) and (27)， we obtain(30)thus(31)(32)hence let μk(x，tm)，vk(x，tm) be distinct solutions of the ordinary differential Eqs.(29) and(30)，then (q，r) determined by (22) is a solution of Eq.(6)with n=m=2 or a solution of Eq.(7) with n=m=3.Based on the form of the function det (W)in Eq.(24)， we introduce the hyperelliptic Riemann surfacewith genus g=N.For the same ， there are two points and on differentsheets of Γ.Since R(λ) is a polynomial of order 2N+2 in terms of λ， there are two infinite points ∞1 and ∞2 which are not branch points of Γ.On Γ we fix a set of regular cycle paths：a1，a2，...，aN；b1，b2，...，bN，which are independent and have the intersection numbers as followsak∘aj=bk∘bj=0，ak∘bj=δkj，k，j=1，…，N.The holomorphic differentials on Γ are chosen to beLet N×N matrices A=(Akj) and B=(Bkj) are invertible.Define matrices C and τ by C=A-1，τ=A-1B.The matrix τ can be shown to be symmetric and has a positive definite imaginary part.We normalize into the following new basisThen we findʃbkωj=τjk.For a fixed point p0, the Abel-Jacobi coordinate are given as follows(33)(34)By using (33) and the first expression of (29), we havewhich givesby use of the following equalityIn a similar way, we get from(29)-(34)Based on the above results we have the followingρ1=Ω1x+Ωmtm+γ1,ρ2=-Ω1x-Ωmtm+γ2,whereWe define an Abel map on Γ as followsA(p)=ω,ω=(ω1，…,ωN)T,A(∑nkpk)=∑nkA(pk).Consider two special divisors m (m=1,2); then we getWe define the Riemann theta function of Γ as(πiτz,z+2πiζ,z),ζ∈CN,in which ζ=(ζ,…,ζN)T,ζ,z terms of the Riemann theorem in algebraic geometry, there exist two constant vectors M1,M2∈CNsuch thatF1=θ(A(p)-ρ1-M1)has exactly N zeros at λ=μ1,...,μN ; andF2=θ(A(p)-ρ2-M2)has exactly N zeros at λ=ν1,...,νN.In order to make these functions single valued, the surface Γ is cut along all ak,bk to form a simply connected region, whose boundary is denoted by γ.Notice the fact that the integralsare constants independent of ρ1 and ρ2withApplying the residue theorem, we have(35)(36)In order to compute the residues in (35) and (36), we first introduce local coordinates z=λ-1at infinity.Then the hyperelliptic curve ξ2=R(λ) in the neighborhood of infinity can be expressed as with is easy to see thatSince the Riemann theta function is an even function，Fm(λ) can be written as(37)where Dj signifies its derivative with respect to the j th argument of is easy to compute that(38)Substituting Eq.(38) into Eq.(37), we arrive atwhich leads toHence we have(39)whereand πs and ηs are constants.From Eqs.(35), (36) and (39), we get(40)Substituting Eq.(40) into Eqs.(22), we finally obtain the following algebraic-geometric solutions of Eq.(6) with n=m=2 or of Eq.(7) with n=m=3,rwhere q0(tm)and r0(tm)are two arbitrary complex functions about variable tm .3 ConclusionsWe obtained a nonlinear NLS-MKdV hierarchy and its Hamiltonian structure by use of the Tu scheme, furthermore, for the convenience of obtaining algebro-geometric solutions, we transform the3×3matrix isospectral problem into an equivalent2×2one, then the algebro-geometric solutions of the coupled NLS equation and coupled MKdV equation are constructed in terms of Riemann theta functions easily.References【相关文献】[1] Gardner C S, Greene J M, Kruskal M D, et al.Method for solving the Korteweg-de Vries equation[J].Phys Rev Lett, 1967,19: 1095-1097.[2] Li Y S.Soliton and Integrable Systems,Advanced Series in NonlinearScience[M].Shanghai: Shanghai Scientific and Technological Education Publishing House, 1999.[3] Hirota R, Satsuma J.A variety of nonlinear network equations generated from theBäcklund transformation f or the Tota lattice[J].Suppl Prog Theor Phys,1976, 59: 64-100.[4] Liu H Z.Exact periodic wave solutions for the hKdV equation[J].Nonlinear Anal, 2009, 70: 2379-2381.[5] Olver P J.Applications of Lie Groups to Differential Equations, in: Grauate Texts in Mathematics[M].New York: Springer, 1993.[6] Bluman G W, Kumei S.Symmetries and Differential Equations[M].Berlin:Springer-Verlag World Publishing Gorp, 1989.[7] Cantwell B J.Introduction to Symmetry Analysis[M].Cambridge:Cambridge University Press, 2002.[8] Liu H Z.Lie symmetry analysis and exact explicit solutions for general Burgers’ equation[J].J Comput Appl Math,2008,228: 1-9.[9] Liu Y, Liu X Q.Symmetry reduction, exact solutions and conservation laws of the(1+1)dimension Caudrey-Dodd-Gibbon equation[J].Journal of Liaocheng University (Natural Science Edition)，2014，27(01)：8-12+24.[10] Li Z Q，Li u H Z.The application of (G′/G)-expansion method for fifth-order dispersive equation [J].Journal of Liaocheng University(Natural Science Edition)，2016，29(04)：1-3+7.[11] Li Y, Li L Q, Li H H，et al.Exact solutions and conservation laws of the(3+1)dimensional Zakharov-Kuznetsov-Burgers equation [J].Journal of Liaocheng University(Natural Science Edition)，2017，30(01)：10-17.[12] Xin X P.Non-local symmetries and exact solutions of nonlinear development equations[J].Journal of Liaocheng University(Natural Science Edition),2018,31(1):15-20.[13] Gesztesy F,Holden H.Soliton Equations and their Algebro-GeometricSolutions[M].Cambridge: Cambridge University Press, 2003.[14] Hou Y,Fan E G.Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy[J].J Math Phys, 2013, 54: 073505-073530.[15] Hou Y, Fan E G, Zhao P.The algebro-geometric solutions for Hunter-Saxton hierarchy[J].Z Angew Math Phys,2013，65(3)：487-520.[16] Hou Y, Zhao P, Fan E G,et al.Algebro-geometric solutions for the Degasperis-Procesi hierarchy[J].SIAM J Math Anal, 2013, 45: 1216-1266.[17] Zhao P, Fan E G,Hou Y.Algebro-Geometric solutions for the Ruijsenaars-Toda hierarchy[J].Chaos Solitons Fractals, 2013, 54: 8-25.[18] Tu G Z.The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems[J].J Math Phys, 1989, 30: 330-338.[19] Zhang Y F,Hon Y C.Some evolution hierarchies derived from self-dual Yang-Mills equations[J].Commun Theor Phys, 2011, 56: 856-872.[20] Zhang Y F,Feng B L.A few Lie algebras and their applications for generating integrable hierarchies of evolution types[J].Commun Nonlinear Sci Numer Simulat,2011, 16(8): 3045-3061.[21] Zhang Y F, Tam H H.An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation[J].Applied Mathematics and Computation, 2013, 219:5837-5848.[22] Wang X Z, Dong H H, Li Y X.Some reductions from a lax integrable system and their hamiltonian structures[J]. Applied Mathematics and Computation,2012, 218:10032-10039.[23] Yang H X, Du J, Xu X X,et al.Hamiltonian and Super-hamiltonian systems of a hierarchy of soliton equations[J]. Applied Mathematics and Computation, 2010, 217: 1497-1508.。

IP101

IP101Single port 10/100 Fast Ethernet Transceiver1.0 Features¢ 10/100Mbps TX/FX¢ Full-duplex or half-duplex¢ Supports Auto MDI/MDIX function¢ Fully compliant with IEEE 802.3/802.3u ¢ Supports IEEE 802.3u auto-negotiation ¢ Supports MII / RMII / SNI interface¢ IEEE 802.3 full duplex control specification ¢ Supports Automatic Power Saving mode¢ Supports BaseLine Wander (BLW) compensation¢ Supports Interrupt function ¢ Supports repeater mode¢ Single 3.3V power supply with built-in 2.5V regulator¢ DSP-based PHY Transceiver technology¢ Using either 25MHz crystal or 50MHz REF_CLK as clock source¢ Flexible LED display for speed, duplex, link, activity and collision¢ Supports flow control to communicate with other MAC through MDC and MDIO ¢ 0.25u, CMOS technology ¢48-pin LQFP2.0 General DescriptionIP101 is an IEEE 802.3/802.3u compliant single-port Fast Ethernet Transceiver for both 100Mbps and 10Mbps operations. It supports Auto MDI/MDIX function to simplify the network installation and reduce the system maintenance cost. To improve the system performance, IP101 provides a hardware interrupt pin to indicate the link, speed and duplex status change. IP101 also provides Media Independent Interface (MII) / Serial Network Interface (SNI) or Reduced Media Independent Interface (RMII) to connect with different types of 10/100Mb Media Access Controller (MAC). IP101 is designed to use category 5 unshielded twisted-pair cable or Fiber-Optic cables connecting to other LAN devices. A PECL interface is supported to connect with an external 100Base-FX fiber optical transceiver.IP101 Transceiver is fabricated with advanced CMOS technology, which the chip only requires 3.3V as power supply and consumes very low power in the Auto Power Saving mode. IP101 can be implemented as Network Interface Adapter with RJ-45 for twisted-pair connection or MAU for Fiber Connection. It can also be easily implemented into HUB, Switch, Router, Access Point, Advanced Communication Riser (ACR) and Communication and Networking Riser (CNR).IP101 3.0 Transmit and Receive Data Path Block DiagramRXITXOConnectorFigure 1: Flow chart of IP101IP1014.0 Pin AssignmentsFigure 2 : IP101 pins assignmentIP101 5.0 Pin DescriptionsType DescriptionLI Latched Input in power up or reset I/O Bi-directional input and outputI InputO Output Type Description PD Internal Pull-DownPU Internal Pull-UpP PowerOD Open DrainPin no. Label Type DescriptionMII and PCS Interface - Management Interface Pins25 MDC I Management Data Interface Clock: This pin provides a clockreference to MDIO. The clock rate can be up to 10MHz.26 MDIO I/O Management Data interface Input/Output: The function of thispin is to transfer management information between PHY andMAC.MII and PCS Interface – Media Independent Interface (MII) Pins2 TX_EN I(PD) Transmit Enable: This pin is an active high input. At high status, it indicates the nibble data in TXD[3:0] is valid.7 TX_CLK O Transmit Clock: This pin provides a continuous 25MHz clock at100Mbps and 2.5Mbps as timing reference for TXD[3:0] andTX_EN when the chip operates under MII and SNI modes. Thispin is an input pin operates as RMII reference clock (REF_CLK)under RMII mode.3, 4, 5, 6 TXD[3:0] I Transmit Data: When TX_EN is set low, MAC will transmit datathrough these 4 lines to PHY which the transmission issynchronizing with TX_CLK.22 RX_DV O Receive Data Valid: At high status stands for data flow is presentwithin RXD[0:3] lines and low means no data exchange occurred.16 RX_CLK O Receive Clock: This pin provides 25MHz for 100Mbpstransmission or 2.5Mhz for 10Mbps transmission and RX_DV pinuses this pin as its reference under MII or SNI mode. While underRMII mode this pin is driven low.18, 19, 20, 21 RXD[3:0] O Receive Data: These 4 data lines are transmission path for PHYto send data to MAC and they are synchronizing with RX_CLK.IP1015.0 Pin Descriptions (continued)Pin no. Label Type DescriptionMII and PCS Interface – Media Independent Interface (MII) Pins24 RX_ER/FIBMOD O/LI(PD)Receive error: This pin outputs a high status when errorsoccurred in the decoded data in the transmission.Fiber Mode: During power on reset, this pin status is latched todetermine at which media mode to operate:1: Fiber mode0: UTP modeAn internal weak pull low resistor sets this to the default of UTPmode. It is possible to use an external 5.1KΩpull high resistor toenable fiber mode.After power on, the pin operates as the Receive Error pin.1 COL/RMII O/LI(PD) Collision Detected: When this pin outputs a high status signal it means collision is detected.RMII Mode: During power on reset, this pin status is latched and arranged with MII/SNIB (pin44) to determine MAC interfaceRMII MII/SNIB1 X RMII Interface0 1 MII Interface0 0 SNII Interface(Notice: This pin is pulled down internally)23 CRS/LEDMOD O(PD)Carrier Sense: When signal output from this pin is high indicates the transmission is in process and at low status means the line is in idle state.LEDMOD: During power on reset, this pin status is latched to determine at which LED mode to operate, please refer to the LED pins description.(Notice: This pin is pulled down internally)RMII (Reduced MII)7 REF_CLK I Reference Clock: This pin is an input pin operates as RMIIreference clock (REF_CLK) under RMII mode. 25MHz CrystalInput and Output, X1 & X2, should be disconnected whenREF_CLK is used as the clock source of IP108.2 TX_EN I(PD)Transmit Enable: For MAC to indicate transmit operation5,6 TXD[1:0] I Transmit two-bit Data24 RX_ER I/O Receive Error22 CRS_DV O Carrier Sense and Receive Data Valid20, 21 RXD[1:0] O Received two-bit DataIP101 5.0 Pin Descriptions (continued)Pin no. Label Type DescriptionSNI (Serial Network Interface): 10Mbps only2 TX_EN I(PD)Transm it Enable: Indicate transmit operation to MAC7 TX_CLK O Transmit Clock: 10MHz, generate either by PHY or by external6 TXD0 I Transmit Serial Data16 RX_CLK O Receive Clock: 10MHz, clock recovery from received data21 RXD0 O Received Serial Data1 COL O Collision Detect23 CRS O Carrier SenseCable Transmission Interface34 33 MDI_TPMDI_TNOOTransmit Output Pair: Differential pair shared by 100Base-TX,100Base-FX and 10Base-T modes.When configured as100Base-TX, output is an MLT-3 encoded waveform. Whenconfigured as 100Base-FX, the output is pseudo-ECL level.31 30 MDI_RPMDI_RNIIReceive Input Pair: Differential pair shared by 100Base-TX,100Base-FX, and 10Base-T modes.IC Configuration Options43 ISOL I(PD) Set high to this pin will isolate IP101 from other MAC. This action will also isolate the MDC/MDIO management interface. The power usage is at minimum when this pin is activated. This pin can be directly connected to GND or VCC. (An internal weak pulled-down is used to be inactive as a default)40 RPTR I(PD) Enable this pin to high will put the IP101 into repeater mode. This pin can be directly connected to GND or VCC. (An internal weak pulled-down is used to be inactive as a default)39 SPD LI/O(PU) This pin is latched to input during a power on or reset condition. Set high to put the IP101 into 100Mbps operation. This pin can be directly connected to GND or VCC. (An internal weak pulled-up is used to set 100Mbps as a default)38 DPLX LI/O(PU) This pin is latched to input during a power on or reset condition. Set high to enable full duplex. This pin can be directly connected to GND or VCC. (An internal weak pulled-up is used to set full duplex as a default)37 AN_ENA LI/O(PU) This pin is latched to input during a power on or reset condition. Set high to enable auto-negotiation mode, set low to force mode. This pin can be directly connected to GND or VCC. (An internal weak pulled-up is used to enable N-WAY as a default)41 APS I(PU) Set high to put the IP101 into APS mode. This pin can be directly connected to GND or VCC. Refer to Section 7.7 for more information. (An internal weak pulled-up is used to enable APS mode as a default)44 MII_SNIB LI/O(PU) This pin is latched to input during a power on or reset condition. Pull high to set the IP101 into MII mode operation. Set low for SNI mode. This pin can be directly connected to GND or VCC. (An internal weak pulled-up is used to set MII mode as a default)IP1015.0 Pin Descriptions (continued)Pin no. Label Type DescriptionLED and PHY Address ConfigurationThese five pins are latched into the IP101 during power up reset to configure PHY address [0:4] used for MII management register interface. And then, in normal operation after initial reset, they are used as driving pins for status indication LED. The driving polarity, active low or active high, is determined by each latched status of the PHY address [4:0] during power-up reset. If latched status is high then it will be active low, and if latched status is Low then it will be active high.Moreover, IP101 provides 2 LED modes. If 2nd LED mode is selected by pulling up pin CRS, only 3 LEDs are needed for status indication. Default is first LED mode.LED mode 1 LED mode 2LED0 LINK LINK /ACT(blinking)LED1 FULL DUPLEX FULL DUPLEX /COL(blinking)LED2 10BT /ACT(blinking) 10BTLED3 100BT /ACT(blinking) 100BTLED4 COL9 PHYAD0/LED0 LI/O PHY Address [0]Status:Mode1: Active when linked.Mode2: Active when linked and blinking when transmitting orreceiving data.10 PHYAD1/LED1 LI/O PHY Address [1]Status:Mode1: Active when in Full Duplex operation.Mode2: Active when in Full Duplex operation and blinking whencollisions occur.12 PHYAD2/LED2 LI/O PHY Address [2]Status:Mode1: Active when linked in 10Base-T mode, and blinking whentransmitting or receiving data.Mode2: Active when linked in 10Base-T mode.13 PHYAD3/LED3 LI/O PHY Address [3]Status:Mode1: Active when linked in 100Base-TX and blinking whentransmitting or receiving data.Mode2: Active when linked in 100Base-TX mode.15 PHYAD4/LED4LI/O PHY Address [4]Status:Mode1: Active when collisions occur.Mode2: Reserved.Clock and Miscellaneous - Crystal Input/Output Pins47 X2 O 25MHz Crystal Output: Connects to crystal to provide the25MHz output. It must be left open when X1 is driven with anexternal 25MHz oscillator. It must be left open when X1 is drivenwith an external 25MHz oscillator or set to low with a pull downresistor.46 X1 I 25MHz Crystal Input: Connects to crystal to provide the 25MHzcrystal input. If a 25MHz oscillator is used, connect X1 to theoscillator’s output. If X1 is set to low with a pull down resistor, a50MHz clock could be applied to pin7 as clock source.IP101 5.0 Pin Descriptions (continued)Pin no. Label Type DescriptionClock and Miscellaneous - Miscellaneous Pins42 RESET_N I RESET_N: Enable a low status signal will reset the chip. For acomplete reset function, this pin must be asserted low for at least10ms.48 INTR I/O(OD) Interrupt Pin: When the MII register 17:<15> is set to high, this pin is used as an interrupt pin (Notice: this is an open drain output, so an external pulled-up resistor is needed)27 TEST_ON (PD) Test Enable: Set this pin to high to enable test mode, while fornormal operation, this pin does not need to be connected. (Aninternal weak pulled-down is used to disable test mode as adefault)28 ISET I Transmit Bias Resistor Connection: This pin should beconnected to GND via a6.2KO (1%) resistor to define drivingcurrent for transmit DAC. The resistance value may be changed,depending on experimental results of the IP101.Power and Ground32 REGOUT P Regulator Power Output: This is a regulator power output forIP101 digital circuitry.36 AVDD33 P 3.3V Analog power input: This is a 3.3V power supply for analogcircuitry, and it should be decoupled carefully.29,35 AGND P Analog Ground: These 2 pins should connect to motherboard’sGND.8 REGIN P Regulator Power Input: This is a regulator power input fromPin32. No external regulator needed.14 DVDD33 P 3.3V Digital Power input: This is a 3.3V power supply for digitalcircuitry.11,17,45 DGND P Digital Ground: These 3 pins should connect to motherboard’sGND.IP1016.0 Register DescriptionsThis section will explain the meaning and usage for each of the registers available in the IP101.The first 7 registers, i.e., Register 0 to Register 6, are defined according to IEEE 802.3 standard, while the rest registers are defined by IC Plus Corp. and they are for internal use or reserved for other usage.The first 2 registers contain the basic control and status register defined by IEEE standard.Each register has its own default value, and it is placed in the right block of each register title.Register 0 : MII Control RegisterAddress Name Description/Usage Default value (h):310015 Reset When set, this action will bring both status and control registersof the PHY to default state. This bit is self-clearing.1 = Software reset0 = Normal operation0, RW14 Loop-back This bit enables loop-back of transmit data to the receive datapath, i.e., TXD to RXD.1 = enable loop-back0 = normal operation0, RW13 SpeedSelection This bit sets the speed of transmission.1 = 100Mbps0 = 10MbpsDuring 100Base-FX mode, and when this bit = 1, it indicatesread only.1, RW12 Auto-NegotiationEnable This bit determines the auto-negotiation function.1 = enable auto-negotiation; bits 13 and 8 will be ignored.0 = disable auto-negotiation; bits 13 and 0:<8> will determinethe link speed and the data transfer mode, under this condition.When 100Base-FX mode is enabled, and this bit=0, it indicatesread only.1, RW11 Power Down This bit will turn down the power of the PHY chip and theinternal crystal oscillator circuit if this bit is enabled. The MDCand MDIO are still activated for accessing to the MAC.1 = power down0 = normal operation0, RW10 Isolate 1=electrically Isolate PHY from MII but not isolate MDC and MDIO0=normal operation0,RW9 Restart Auto-Negotiation This bit allows the Nway auto-negotiation function to be reset.1 = restart auto-negotiation0 = normal operation0, RW8 Duplex Mode This bit sets the duplex mode if auto-negotiation is disabled (bit12=0)1 = full duplex0 = half duplexAfter completing auto-negotiation, this bit will reflect the duplexstatus.(1: Full duplex, 0: Half duplex)When 100Base-FX mode is enabled, this bit can be setthrough the MDC/MDIO SMI interface or DUPLEX pin.1, RW7 Collision Test 1=enable COL signal test0=disable COL signal test0,RW 6:0 ReservedIP101 6.0 Register Descriptions (continued)Register 1 : MII Status RegisterAddress Name Description/Usage Default value (h):784915 100Base-T4 1 = enable 100Base-T4 support0 = suppress 100Base-T4 support0, RO14 100Base-TXFull Duplex 1 = enable 100Base-TX f ull duplex support0 = suppress 100Base-TX full duplex support1, RO13 100BASE-TXHalf Duplex 1 = enable 100Base-TX half duplex support0 = suppress 100Base-TX half duplex support1, RO12 10Base-T FullDuplex 1 = enable 10Base-T full duplex support0 = suppress 10Base-T full duplex support1, RO11 10_Base-THalf Duplex 1 = enable 10Base-T half duplex support0 = suppress 10Base-T half duplex support1, RO10:7 Reserved 0, RO6 MF PreambleSuppression The IP101 will accept management frames with preamble suppressed. The IP101 accepts management frames withoutpreamble. A Minimum of 32 preamble bits are required for thefirst SMI read/write transaction after reset. One idle bit isrequired between any two management transactions as perIEEE802.3u specifications1, RO5 Auto-NegotiationComplete 1 = auto-negotiation process completed0 = auto-negotiation process not completed0, RO4 Remote Fault 1 = remote fault condition detected (cleared on read)0 = no remote fault condition detectedWhen in 100Base-FX mode, this bit means an in-band signalFar-End-Fault is detected.0, RO/LH3 Auto-Negotiation 1 = Link had not been experienced fail state0 = Link had been experienced fail state1, RO2 Link Status 1 = valid link established0 = no valid link established0, RO/LL1 Jabber Detect 1 = jabber condition detected0 = no jabber condition detected0, RO/LH0 ExtendedCapability 1 = extended register capability0 = basic register capability only1, RO6.0 Register Descriptions (continued) Register 2 : PHY Identifier Register 1Address Name Description/Usage Default value (h):024315:0 PHYID1 PHY identifier ID for software recognize IP101 0X0243, RO Register 3 : PHY Identifier Register 2Address Name Description/Usage Default value (h):0C5015:0 PHYID2 PHY identifier ID for software recognize 0X0C50, RO Note : Register 2 and register 3 identifier registers altogether consist of Vender model, model revision number and Organizationally Unique identifier (OUI) information. T otal of 32 bits allocate in these 2 registers and they can return all zeroes in all bits if desired. Register 2 contains OUI’s most significant bits and OUI’s lest significant bits, Vender model, Model revision number are allocated in register 3.IP101 6.0 Register Descriptions (continued)Register 4 lists the advertised abilities during auto-negotiation for what will be transmitted to IP101’s Link Partner. Register 4 : Auto-Negotiation Advertisement RegisterAddress Name Description/Usage Default value (h):000115 NP Next Page bit.0 = transmitting the primary capability data page1 = transmitting the protocol specific data page0, RO14 Reserved 0, RO 13 RF 1 = advertise remote fault detection capability0 = do not advertise remote fault detection capability0, RW12 Reserved 0, RO11 Asymmetric.Pause 1 = asymmetric flow control is supported by local node0 = asymmetric flow control is NOT supported by local node0, RW10 Pause 1 = flow control is supported by local node0 = flow control is NOT supported by local node0, RW9 T4 1 = 100Base-T4 is supported by local node0 = 100Base-T4 not supported by local node0, RO8 TX FullDuplex 1 = 100Base-TX full duplex is supported by local node0 = 100Base-TX full duplex not supported by local node1, RW7 TX 1 = 100Base-TX is supported by local node0 = 100Base-TX not supported by local node1, RW6 10 FullDuplex 1 = 10Base-T full duplex supported by local node0 = 10Base-T full duplex not supported by local node1, RW5 10 1 = 10Base-T is supported by local node0 = 10Base-T not supported by local node1, RW4:0 Selector Binary encoded selector supported by this node. Currentlyonly CSMA/CD <00001> is specified. No other protocols aresupported.<00001>, RO6.0 Register Descriptions (continued)Register 5 describes the advertised abilities of the Link Partner’s PHY when it is receiving data during the process of auto-negotiation. If next-pages are supported, this register may change after the auto-negotiation has established. Register 5 : Auto-Negotiation Link Partner Ability RegisterAddress Name Description/Usage Default value (h):008015 Next Page Next Page bit.0 = transmitting the primary capability data page1 = transmitting the protocol specific data page0, RO14 Acknowledge 1 = link partner acknowledges reception of local node’scapability data word0 = no acknowledgement0, RO13 Remote Fault 1 = link partner is indicating a remote fault0 = link partner does not indicate a remote fault0, RO 12 Reserved 0, RO11 Asymmetric.Pause 1 = asymmetric flow control is supported by local node0 = asymmetric flow control is NOT supported by local node0, RO10 Pause 1 = flow control is supported by Link partner0 = flow control is NOT supported by Link partner0, RO9 T4 1 = 100Base-T4 is supported by link partner0 = 100Base-T4 not supported by link partner0, RO8 TXFD 1 = 100Base-TX full duplex is supported by link partner0 = 100Base-TX full duplex not supported by link partner0, RO7 100BASE-TX 1 = 100Base-TX is supported by link partner0 = 100Base-TX not supported by link partnerThis bit will also be set after the link in 100Base is establishedby parallel detection.1, RO6 10FD 1 = 10Base-T full duplex is supported by link partner0 = 10Base-T full duplex not supported by link partner0, RO5 10Base-T 1 = 10Base-T is supported by link partner0 = 10Base-T not supported by link partnerThis bit will also be set after the link in 10Base is establishedby parallel detection.0, RO4:0 Selector Link Partner’s binary encoded node selector Currently onlyCSMA/CD <00001> is specified<00000>, ROIP101 6.0 Register Descriptions (continued)Register 6 defines more auto-negotiation registers to meet the requirement.Register 6 : Auto-Negotiation Expansion RegisterAddress Name Description/Usage Default value (h):000015:5 Reserved This bit is always set to 0.4 MLF This status indicates if a multiple link fault has occurred.1 = fault occurred0 = no fault occurred0, RO3 LP_NP_ABLE This status indicates if the link partner supports Next Pagenegotiation.1 = supported0 = not supported0, RO2 NP_ABLE This bit indicates if the device is able to send additional NextPages.0, RO1 PAGE_RX This bit will be set if a new link code word page has beenreceived. It is cleared automatically after the auto-negotiationlink partner’s ability register (register 5) is read by themanagement.0, RO 0 LP_NW_ABLE 1 = link partner supports Nway auto-negotiation. 0, RO6.0 Register Descriptions (continued)Register 16 and register 17 are defined by IC Plus Corp. and it is for internal testing purpose. Register 16 : PHY Spec. Control RegisterAddress Name Description/Usage Default value (h):000015 Debug Mode 0 = IP101 operates at normal mode1 = IP101 operates at debug mode(Notice the functionalities of bit 16:<14>, 16:<13>, 16:<12>,and 16:<4:0> depend on the setting of this bit 16:<15>0, R/W14:12 Reserved11 MDI disable Set high to disable the automatic switch of MDI and MDI-Xmodes0, R/W10 Heart BeatEnableHeart beat function enable at 10Base-T 0, R/W9 JabberEnableJabber function enable at 10Base-T 0, R/W8 Far-End FaultEnable/Disable To enable or disable the functionality of Far-End FaultMode Enable Disable100Base-TX 1 0100Base-FX 0 10, R/W7 AnalogPower SavingDisableSet high to disable the power saving during auto-negotiation 0, R/W 6 Reserved 0, R/W5 Bypass DSPreset Set high to bypass the reset DSP mechanism in PCSsub-layer0, R/W4:3 Reserved2 RepeaterModeSet high to put IP101 into repeater mode 0, R/W 1 APS Mode Set high to enable Auto Power Saving mode 0, R/W 0 Analog Off Set high to power down analog transceiver 0, R/WIP101 6.0 Register Descriptions (continued)Register 17 : PHY Interrupt Ctrl/Status RegisterAddress Name Description/Usage Default value (h):0E0015 INTR pinused Set high to enable pin48 as an interrupt pin, or highimpedance is presented at this pin0, R/W14:12 Reserved11 All Mask When this bit is set high, changes in all events will not causean interrupt1, R/W10 Speed Mask When this bit is set high, changes in speed mode will notcause an interrupt1, R/W9 Duplex Mask When this bit is set high, changes in duplex mode will notcause an interrupt1, R/W8 Link Mask When this bit is set high, changes in link status will not causean interrupt1, R/W7 Arbiter StateEnable When this bit is set high, changes in N-WAY arbiter statemachine will cause an interrupt0, R/W6 Arbiter StateChangeFlag to indicate N-WAY arbiter change interrupt 0, R/W 5:3 Reserved 0, R/W2 Link StatusChangeFlag to indicate link status change interrupt 0, R/W1 SpeedChangeFlag to indicate speed change interrupt 0, R/W0 DuplexChangeFlag to indicate duplex change interrupt 0, R/W7.0 Functional DescriptionIP101 10/100Mbps Ethernet PHY Transceiver integrates 100 Base-TX, 100 Base-FX and 10 Base-T modules into a single chip. IP101 acts as an interface between physical signaling and Media Access Controller (MAC).IP101 has several major functions:1. PCS layer (Physical Coding Sub-Layer): Thisfunction contains transmit, receive and carrier sense functional circuitries.2. Management interface: Media IndependentInterface (MII) or Reduced Management Interface (RMII) registers contains information for communication with other MAC.3. Auto-Negotiation: Communication conditionsbetween 2 PHY transceivers. IP101 advertise its own ability and also detects corresponding operational mode from the other party, eventually both sides will come to an agreement for their optimized transmission mode.IP101’s major features included:1. Flow Control ability2. LED configuration access3. Operation modes for both full and half duplex4. APS (Auto Power Saving) mode5. Base Line Wander (BLW) compensation6. Auto MDI/MDIX function7. Interrupt function8. Repeater ModeMajor Functional Block DescriptionThe functional blocks diagram is referred to Figure 1: 1. 4B/5B encoder: 100 Base-X transmissions requireconverting 4-bit nibble data into 5-bit wide data code-word format. Transmitting data is packaged by J/K codes at the start of packet and by T/R codes at the end of packet in the 4B/5B block.When transmit error has occurred during a transmitting process, the H error code will be sent.The idle code is sent between two packets.2. 4B/5B Decoder: The decoder performs the 5B/4Bdecoding from the received code-groups. The 5 bits(5B) data is decoded into four bits nibble data. The decoded 4 bit (4B) data is then forwarded through MII to the repeater, switch or MAC device. The SSD is then converted into 4B 5 nibbles and the ESD and IDLE Codes are replaced by 4B 0 nibbles data.The decoded data is driven onto the corresponding MII port or shared MII port. Receiving an invalid code group will cause PHY to assert the MII RXER signal.3. Scrambler/Descrambler: Repetitive patterns existin 4B/5B encoded data which result in large RF spectrum peaks and keep the system from being approved by regulatory agencies. The peak in the radiated signal is reduced significantly by scrambling the transmitted signal. Scrambler addsa random generator to the data signal output. Theresulting signal is with fewer repetitive data patterns. The scrambled data stream is descrambled at the receiver by adding another random generator to the output. The receiver’s random generator has the same function as the transmitter’s random generator. Scrambler operation is dictated by the 100Base-X and TP_FDDI standards.4. NRZI/MLT-3(Manchester) Encoder and Decoder:100 Base-TX Transmission requires to encode the data into NRZ format and again converted into MLT-3 signal, while 10 Base-T will convert into Manchester form after NRZ coding. This helps to remove the high frequency noise generated by the twisted pair cables. At receiving end, the coding is reversed from MLT-3 (Manchester) signal back to NRZ format.5. Clock Recovery:The receiver circuit recoversdata from the input stream by regenerating clocking information embedded in the serial stream. The clock recovery block extracts the RXCLK from the transition of received6. DSP Engine: This block includes Adaptiveequalizer and Base Line Wander correction function.。

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